linear_algebra.matrix.basis ⟷ Mathlib.LinearAlgebra.Matrix.Basis

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

@@ -239,7 +239,7 @@ theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
   by
   have := basis_toMatrix_mul_linearMap_toMatrix b₃ b₁ b₂ (Matrix.toLin b₃ b₂ A)
-  rwa [LinearMap.toMatrix_toLin] at this 
+  rwa [LinearMap.toMatrix_toLin] at this
 #align basis_to_matrix_mul basis_toMatrix_mul
 -/
 
@@ -249,7 +249,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
     A ⬝ b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) :=
   by
   have := linearMap_toMatrix_mul_basis_toMatrix b₂ b₁ b₃ (Matrix.toLin b₁ b₃ A)
-  rwa [LinearMap.toMatrix_toLin] at this 
+  rwa [LinearMap.toMatrix_toLin] at this
 #align mul_basis_to_matrix mul_basis_toMatrix
 -/
 

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

@@ -255,7 +255,12 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 
 #print basis_toMatrix_basisFun_mul /-
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
-    b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by classical
+    b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
+  classical
+  simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
+  ext i j
+  rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
+    Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 -/
 

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

@@ -255,12 +255,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 
 #print basis_toMatrix_basisFun_mul /-
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
-    b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
-  classical
-  simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
-  ext i j
-  rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
-    Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
+    b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by classical
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
-import Mathbin.LinearAlgebra.Matrix.Reindex
-import Mathbin.LinearAlgebra.Matrix.ToLin
+import LinearAlgebra.Matrix.Reindex
+import LinearAlgebra.Matrix.ToLin
 
 #align_import linear_algebra.matrix.basis from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.basis
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Matrix.Reindex
 import Mathbin.LinearAlgebra.Matrix.ToLin
 
+#align_import linear_algebra.matrix.basis from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
 /-!
 # Bases and matrices
 

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

@@ -89,7 +89,7 @@ theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M)
 #print Basis.coePiBasisFun.toMatrix_eq_transpose /-
 -- TODO (maybe) Adjust the definition of `basis.to_matrix` to eliminate the transpose.
 theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
-    ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by ext (M i j);
+    ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by ext M i j;
   rfl
 #align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transpose
 -/
@@ -99,7 +99,7 @@ theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
 theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   by
   rw [Basis.toMatrix]
-  ext (i j)
+  ext i j
   simp [Basis.equivFun, Matrix.one_apply, Finsupp.single_apply, eq_comm]
 #align basis.to_matrix_self Basis.toMatrix_self
 -/
@@ -108,7 +108,7 @@ theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) :=
   by
-  ext (i' k)
+  ext i' k
   rw [Basis.toMatrix, Matrix.updateColumn_apply, e.to_matrix_apply]
   split_ifs
   · rw [h, update_same j x v]
@@ -122,7 +122,7 @@ theorem toMatrix_update [DecidableEq ι'] (x : M) :
 theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι → R₂ˣ) :
     e.toMatrix (e.units_smul w) = diagonal (coe ∘ w) :=
   by
-  ext (i j)
+  ext i j
   by_cases h : i = j
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def]
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def, Ne.symm h]
@@ -170,13 +170,13 @@ def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix
     where
   toFun := e.toMatrix
   map_add' v w := by
-    ext (i j)
+    ext i j
     change _ = _ + _
     rw [e.to_matrix_apply, Pi.add_apply, LinearEquiv.map_add]
     rfl
   map_smul' := by
     intro c v
-    ext (i j)
+    ext i j
     rw [e.to_matrix_apply, Pi.smul_apply, LinearEquiv.map_smul]
     rfl
   invFun m j := ∑ i, m i j • e i
@@ -186,7 +186,7 @@ def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix
     exact e.sum_to_matrix_smul_self v j
   right_inv := by
     intro m
-    ext (k l)
+    ext k l
     simp only [e.to_matrix_apply, ← e.equiv_fun_apply, ← e.equiv_fun_symm_apply,
       LinearEquiv.apply_symm_apply]
 #align basis.to_matrix_equiv Basis.toMatrixEquiv
@@ -261,7 +261,7 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
   classical
   simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
-  ext (i j)
+  ext i j
   rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
     Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
@@ -300,7 +300,7 @@ theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' 
   have := Classical.decEq ι
   have := Classical.decEq ι'
   haveI := Classical.decEq ι''
-  ext (i j)
+  ext i j
   simp only [Matrix.mul_apply, Basis.toMatrix_apply, Basis.sum_repr_mul_repr]
 #align basis.to_matrix_mul_to_matrix Basis.toMatrix_mul_toMatrix
 -/

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

@@ -67,25 +67,34 @@ variable (e : Basis ι R M) (v : ι' → M) (i : ι) (j : ι')
 
 namespace Basis
 
+#print Basis.toMatrix_apply /-
 theorem toMatrix_apply : e.toMatrix v i j = e.repr (v j) i :=
   rfl
 #align basis.to_matrix_apply Basis.toMatrix_apply
+-/
 
+#print Basis.toMatrix_transpose_apply /-
 theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
   funext fun _ => rfl
 #align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_apply
+-/
 
+#print Basis.toMatrix_eq_toMatrix_constr /-
 theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M) :
     e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) := by ext;
   rw [Basis.toMatrix_apply, LinearMap.toMatrix_apply, Basis.constr_basis]
 #align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constr
+-/
 
+#print Basis.coePiBasisFun.toMatrix_eq_transpose /-
 -- TODO (maybe) Adjust the definition of `basis.to_matrix` to eliminate the transpose.
 theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
     ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by ext (M i j);
   rfl
 #align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transpose
+-/
 
+#print Basis.toMatrix_self /-
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   by
@@ -93,7 +102,9 @@ theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   ext (i j)
   simp [Basis.equivFun, Matrix.one_apply, Finsupp.single_apply, eq_comm]
 #align basis.to_matrix_self Basis.toMatrix_self
+-/
 
+#print Basis.toMatrix_update /-
 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) :=
   by
@@ -103,7 +114,9 @@ theorem toMatrix_update [DecidableEq ι'] (x : M) :
   · rw [h, update_same j x v]
   · rw [update_noteq h]
 #align basis.to_matrix_update Basis.toMatrix_update
+-/
 
+#print Basis.toMatrix_unitsSMul /-
 /-- The basis constructed by `units_smul` has vectors given by a diagonal matrix. -/
 @[simp]
 theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι → R₂ˣ) :
@@ -114,19 +127,25 @@ theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι →
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def]
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def, Ne.symm h]
 #align basis.to_matrix_units_smul Basis.toMatrix_unitsSMul
+-/
 
+#print Basis.toMatrix_isUnitSMul /-
 /-- The basis constructed by `is_unit_smul` has vectors given by a diagonal matrix. -/
 @[simp]
 theorem toMatrix_isUnitSMul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι → R₂}
     (hw : ∀ i, IsUnit (w i)) : e.toMatrix (e.isUnitSMul hw) = diagonal w :=
   e.toMatrix_unitsSMul _
 #align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSMul
+-/
 
+#print Basis.sum_toMatrix_smul_self /-
 @[simp]
 theorem sum_toMatrix_smul_self [Fintype ι] : ∑ i : ι, e.toMatrix v i j • e i = v j := by
   simp_rw [e.to_matrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
+-/
 
+#print Basis.toMatrix_map_vecMul /-
 theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v :=
   by
@@ -134,12 +153,15 @@ theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b
   simp_rw [vec_mul, dot_product, Matrix.map_apply, ← Algebra.commutes, ← Algebra.smul_def,
     sum_to_matrix_smul_self]
 #align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMul
+-/
 
+#print Basis.toLin_toMatrix /-
 @[simp]
 theorem toLin_toMatrix [Fintype ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
     Matrix.toLin v e (e.toMatrix v) = id :=
   v.ext fun i => by rw [to_lin_self, id_apply, e.sum_to_matrix_smul_self]
 #align basis.to_lin_to_matrix Basis.toLin_toMatrix
+-/
 
 #print Basis.toMatrixEquiv /-
 /-- From a basis `e : ι → M`, build a linear equivalence between families of vectors `v : ι → M`,
@@ -186,6 +208,7 @@ section Fintype
 
 variable [Fintype ι'] [Fintype κ] [Fintype κ']
 
+#print basis_toMatrix_mul_linearMap_toMatrix /-
 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
@@ -194,28 +217,36 @@ theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
       haveI := Classical.decEq κ' <;>
         rw [to_lin_to_matrix, to_lin_mul b' c' c, to_lin_to_matrix, c.to_lin_to_matrix, id_comp])
 #align basis_to_matrix_mul_linear_map_to_matrix basis_toMatrix_mul_linearMap_toMatrix
+-/
 
 variable [Fintype ι]
 
+#print linearMap_toMatrix_mul_basis_toMatrix /-
 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c' f :=
   (Matrix.toLin b c').Injective
     (by rw [to_lin_to_matrix, to_lin_mul b b' c', to_lin_to_matrix, b'.to_lin_to_matrix, comp_id])
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
+-/
 
+#print basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix /-
 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c f := by
   rw [basis_toMatrix_mul_linearMap_toMatrix, linearMap_toMatrix_mul_basis_toMatrix]
 #align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
+-/
 
+#print basis_toMatrix_mul /-
 theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
   by
   have := basis_toMatrix_mul_linearMap_toMatrix b₃ b₁ b₂ (Matrix.toLin b₃ b₂ A)
   rwa [LinearMap.toMatrix_toLin] at this 
 #align basis_to_matrix_mul basis_toMatrix_mul
+-/
 
+#print mul_basis_toMatrix /-
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
     A ⬝ b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) :=
@@ -223,7 +254,9 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
   have := linearMap_toMatrix_mul_basis_toMatrix b₂ b₁ b₃ (Matrix.toLin b₁ b₃ A)
   rwa [LinearMap.toMatrix_toLin] at this 
 #align mul_basis_to_matrix mul_basis_toMatrix
+-/
 
+#print basis_toMatrix_basisFun_mul /-
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
   classical
@@ -232,7 +265,9 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
   rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
     Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
+-/
 
+#print LinearMap.toMatrix_id_eq_basis_toMatrix /-
 /-- A generalization of `linear_map.to_matrix_id`. -/
 @[simp]
 theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
@@ -241,7 +276,9 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
   haveI := Classical.decEq ι'
   rw [← @basis_toMatrix_mul_linearMap_toMatrix _ _ ι, to_matrix_id, Matrix.mul_one]
 #align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrix
+-/
 
+#print Basis.toMatrix_reindex' /-
 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
     (e : ι ≃ ι') : (b.reindex e).toMatrix v = Matrix.reindexAlgEquiv _ e (b.toMatrix (v ∘ e)) := by
@@ -250,9 +287,11 @@ theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι
     Matrix.reindex_apply, Matrix.submatrix_apply, Function.comp_apply, e.apply_symm_apply,
     Finsupp.mapDomain_equiv_apply]
 #align basis.to_matrix_reindex' Basis.toMatrix_reindex'
+-/
 
 end Fintype
 
+#print Basis.toMatrix_mul_toMatrix /-
 /-- A generalization of `basis.to_matrix_self`, in the opposite direction. -/
 @[simp]
 theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' → M) :
@@ -264,30 +303,39 @@ theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' 
   ext (i j)
   simp only [Matrix.mul_apply, Basis.toMatrix_apply, Basis.sum_repr_mul_repr]
 #align basis.to_matrix_mul_to_matrix Basis.toMatrix_mul_toMatrix
+-/
 
+#print Basis.toMatrix_mul_toMatrix_flip /-
 /-- `b.to_matrix b'` and `b'.to_matrix b` are inverses. -/
 theorem Basis.toMatrix_mul_toMatrix_flip [DecidableEq ι] [Fintype ι'] :
     b.toMatrix b' ⬝ b'.toMatrix b = 1 := by rw [Basis.toMatrix_mul_toMatrix, Basis.toMatrix_self]
 #align basis.to_matrix_mul_to_matrix_flip Basis.toMatrix_mul_toMatrix_flip
+-/
 
+#print Basis.invertibleToMatrix /-
 /-- A matrix whose columns form a basis `b'`, expressed w.r.t. a basis `b`, is invertible. -/
 def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂ M₂) :
     Invertible (b.toMatrix b') :=
   ⟨b'.toMatrix b, Basis.toMatrix_mul_toMatrix_flip _ _, Basis.toMatrix_mul_toMatrix_flip _ _⟩
 #align basis.invertible_to_matrix Basis.invertibleToMatrix
+-/
 
+#print Basis.toMatrix_reindex /-
 @[simp]
 theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι') :
     (b.reindex e).toMatrix v = (b.toMatrix v).submatrix e.symm id := by ext;
   simp only [Basis.toMatrix_apply, Basis.repr_reindex, Matrix.submatrix_apply, id.def,
     Finsupp.mapDomain_equiv_apply]
 #align basis.to_matrix_reindex Basis.toMatrix_reindex
+-/
 
+#print Basis.toMatrix_map /-
 @[simp]
 theorem Basis.toMatrix_map (b : Basis ι R M) (f : M ≃ₗ[R] N) (v : ι → N) :
     (b.map f).toMatrix v = b.toMatrix (f.symm ∘ v) := by ext;
   simp only [Basis.toMatrix_apply, Basis.map, LinearEquiv.trans_apply]
 #align basis.to_matrix_map Basis.toMatrix_map
+-/
 
 end MulLinearMapToMatrix
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -123,7 +123,7 @@ theorem toMatrix_isUnitSMul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι 
 #align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSMul
 
 @[simp]
-theorem sum_toMatrix_smul_self [Fintype ι] : (∑ i : ι, e.toMatrix v i j • e i) = v j := by
+theorem sum_toMatrix_smul_self [Fintype ι] : ∑ i : ι, e.toMatrix v i j • e i = v j := by
   simp_rw [e.to_matrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 

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

@@ -227,10 +227,10 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
   classical
-    simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
-    ext (i j)
-    rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
-      Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
+  simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
+  ext (i j)
+  rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
+    Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 
 /-- A generalization of `linear_map.to_matrix_id`. -/

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

@@ -213,7 +213,7 @@ theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
   by
   have := basis_toMatrix_mul_linearMap_toMatrix b₃ b₁ b₂ (Matrix.toLin b₃ b₂ A)
-  rwa [LinearMap.toMatrix_toLin] at this
+  rwa [LinearMap.toMatrix_toLin] at this 
 #align basis_to_matrix_mul basis_toMatrix_mul
 
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
@@ -221,7 +221,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
     A ⬝ b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) :=
   by
   have := linearMap_toMatrix_mul_basis_toMatrix b₂ b₁ b₃ (Matrix.toLin b₁ b₃ A)
-  rwa [LinearMap.toMatrix_toLin] at this
+  rwa [LinearMap.toMatrix_toLin] at this 
 #align mul_basis_to_matrix mul_basis_toMatrix
 
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :

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

@@ -42,9 +42,9 @@ noncomputable section
 
 open LinearMap Matrix Set Submodule
 
-open BigOperators
+open scoped BigOperators
 
-open Matrix
+open scoped Matrix
 
 section BasisToMatrix
 

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

@@ -67,46 +67,25 @@ variable (e : Basis ι R M) (v : ι' → M) (i : ι) (j : ι')
 
 namespace Basis
 
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-<too large>
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 theorem toMatrix_apply : e.toMatrix v i j = e.repr (v j) i :=
   rfl
 #align basis.to_matrix_apply Basis.toMatrix_apply
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_applyₓ'. -/
 theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
   funext fun _ => rfl
 #align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_apply
 
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 theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M) :
     e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) := by ext;
   rw [Basis.toMatrix_apply, LinearMap.toMatrix_apply, Basis.constr_basis]
 #align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constr
 
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 -- TODO (maybe) Adjust the definition of `basis.to_matrix` to eliminate the transpose.
 theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
     ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by ext (M i j);
   rfl
 #align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transpose
 
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 @[simp]
 theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   by
@@ -115,9 +94,6 @@ theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   simp [Basis.equivFun, Matrix.one_apply, Finsupp.single_apply, eq_comm]
 #align basis.to_matrix_self Basis.toMatrix_self
 
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 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) :=
   by
@@ -128,12 +104,6 @@ theorem toMatrix_update [DecidableEq ι'] (x : M) :
   · rw [update_noteq h]
 #align basis.to_matrix_update Basis.toMatrix_update
 
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 /-- The basis constructed by `units_smul` has vectors given by a diagonal matrix. -/
 @[simp]
 theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι → R₂ˣ) :
@@ -145,12 +115,6 @@ theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι →
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def, Ne.symm h]
 #align basis.to_matrix_units_smul Basis.toMatrix_unitsSMul
 
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 /-- The basis constructed by `is_unit_smul` has vectors given by a diagonal matrix. -/
 @[simp]
 theorem toMatrix_isUnitSMul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι → R₂}
@@ -158,23 +122,11 @@ theorem toMatrix_isUnitSMul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι 
   e.toMatrix_unitsSMul _
 #align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSMul
 
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 @[simp]
 theorem sum_toMatrix_smul_self [Fintype ι] : (∑ i : ι, e.toMatrix v i j • e i) = v j := by
   simp_rw [e.to_matrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 
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 theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v :=
   by
@@ -183,9 +135,6 @@ theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b
     sum_to_matrix_smul_self]
 #align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMul
 
-/- warning: basis.to_lin_to_matrix -> Basis.toLin_toMatrix is a dubious translation:
-<too large>
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 @[simp]
 theorem toLin_toMatrix [Fintype ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
     Matrix.toLin v e (e.toMatrix v) = id :=
@@ -237,9 +186,6 @@ section Fintype
 
 variable [Fintype ι'] [Fintype κ] [Fintype κ']
 
-/- warning: basis_to_matrix_mul_linear_map_to_matrix -> basis_toMatrix_mul_linearMap_toMatrix is a dubious translation:
-<too large>
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 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
@@ -251,9 +197,6 @@ theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
 
 variable [Fintype ι]
 
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 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c' f :=
@@ -261,17 +204,11 @@ theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι']
     (by rw [to_lin_to_matrix, to_lin_mul b b' c', to_lin_to_matrix, b'.to_lin_to_matrix, comp_id])
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
 
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-<too large>
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 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c f := by
   rw [basis_toMatrix_mul_linearMap_toMatrix, linearMap_toMatrix_mul_basis_toMatrix]
 #align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
 
-/- warning: basis_to_matrix_mul -> basis_toMatrix_mul is a dubious translation:
-<too large>
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 theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
   by
@@ -279,9 +216,6 @@ theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis
   rwa [LinearMap.toMatrix_toLin] at this
 #align basis_to_matrix_mul basis_toMatrix_mul
 
-/- warning: mul_basis_to_matrix -> mul_basis_toMatrix is a dubious translation:
-<too large>
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 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
     A ⬝ b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) :=
@@ -290,9 +224,6 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
   rwa [LinearMap.toMatrix_toLin] at this
 #align mul_basis_to_matrix mul_basis_toMatrix
 
-/- warning: basis_to_matrix_basis_fun_mul -> basis_toMatrix_basisFun_mul is a dubious translation:
-<too large>
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 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
   classical
@@ -302,9 +233,6 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
       Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 
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 /-- A generalization of `linear_map.to_matrix_id`. -/
 @[simp]
 theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
@@ -314,9 +242,6 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
   rw [← @basis_toMatrix_mul_linearMap_toMatrix _ _ ι, to_matrix_id, Matrix.mul_one]
 #align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrix
 
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 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
     (e : ι ≃ ι') : (b.reindex e).toMatrix v = Matrix.reindexAlgEquiv _ e (b.toMatrix (v ∘ e)) := by
@@ -328,12 +253,6 @@ theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι
 
 end Fintype
 
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 /-- A generalization of `basis.to_matrix_self`, in the opposite direction. -/
 @[simp]
 theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' → M) :
@@ -346,35 +265,17 @@ theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' 
   simp only [Matrix.mul_apply, Basis.toMatrix_apply, Basis.sum_repr_mul_repr]
 #align basis.to_matrix_mul_to_matrix Basis.toMatrix_mul_toMatrix
 
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 /-- `b.to_matrix b'` and `b'.to_matrix b` are inverses. -/
 theorem Basis.toMatrix_mul_toMatrix_flip [DecidableEq ι] [Fintype ι'] :
     b.toMatrix b' ⬝ b'.toMatrix b = 1 := by rw [Basis.toMatrix_mul_toMatrix, Basis.toMatrix_self]
 #align basis.to_matrix_mul_to_matrix_flip Basis.toMatrix_mul_toMatrix_flip
 
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 /-- A matrix whose columns form a basis `b'`, expressed w.r.t. a basis `b`, is invertible. -/
 def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂ M₂) :
     Invertible (b.toMatrix b') :=
   ⟨b'.toMatrix b, Basis.toMatrix_mul_toMatrix_flip _ _, Basis.toMatrix_mul_toMatrix_flip _ _⟩
 #align basis.invertible_to_matrix Basis.invertibleToMatrix
 
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 @[simp]
 theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι') :
     (b.reindex e).toMatrix v = (b.toMatrix v).submatrix e.symm id := by ext;
@@ -382,9 +283,6 @@ theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι
     Finsupp.mapDomain_equiv_apply]
 #align basis.to_matrix_reindex Basis.toMatrix_reindex
 
-/- warning: basis.to_matrix_map -> Basis.toMatrix_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map Basis.toMatrix_mapₓ'. -/
 @[simp]
 theorem Basis.toMatrix_map (b : Basis ι R M) (f : M ≃ₗ[R] N) (v : ι → N) :
     (b.map f).toMatrix v = b.toMatrix (f.symm ∘ v) := by ext;

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

@@ -85,9 +85,7 @@ theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constrₓ'. -/
 theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M) :
-    e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) :=
-  by
-  ext
+    e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) := by ext;
   rw [Basis.toMatrix_apply, LinearMap.toMatrix_apply, Basis.constr_basis]
 #align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constr
 
@@ -99,9 +97,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transposeₓ'. -/
 -- TODO (maybe) Adjust the definition of `basis.to_matrix` to eliminate the transpose.
 theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
-    ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose :=
-  by
-  ext (M i j)
+    ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by ext (M i j);
   rfl
 #align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transpose
 
@@ -323,9 +319,8 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex' Basis.toMatrix_reindex'ₓ'. -/
 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
-    (e : ι ≃ ι') : (b.reindex e).toMatrix v = Matrix.reindexAlgEquiv _ e (b.toMatrix (v ∘ e)) :=
-  by
-  ext
+    (e : ι ≃ ι') : (b.reindex e).toMatrix v = Matrix.reindexAlgEquiv _ e (b.toMatrix (v ∘ e)) := by
+  ext;
   simp only [Basis.toMatrix_apply, Basis.repr_reindex, Matrix.reindexAlgEquiv_apply,
     Matrix.reindex_apply, Matrix.submatrix_apply, Function.comp_apply, e.apply_symm_apply,
     Finsupp.mapDomain_equiv_apply]
@@ -382,9 +377,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex Basis.toMatrix_reindexₓ'. -/
 @[simp]
 theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι') :
-    (b.reindex e).toMatrix v = (b.toMatrix v).submatrix e.symm id :=
-  by
-  ext
+    (b.reindex e).toMatrix v = (b.toMatrix v).submatrix e.symm id := by ext;
   simp only [Basis.toMatrix_apply, Basis.repr_reindex, Matrix.submatrix_apply, id.def,
     Finsupp.mapDomain_equiv_apply]
 #align basis.to_matrix_reindex Basis.toMatrix_reindex
@@ -394,9 +387,7 @@ theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map Basis.toMatrix_mapₓ'. -/
 @[simp]
 theorem Basis.toMatrix_map (b : Basis ι R M) (f : M ≃ₗ[R] N) (v : ι → N) :
-    (b.map f).toMatrix v = b.toMatrix (f.symm ∘ v) :=
-  by
-  ext
+    (b.map f).toMatrix v = b.toMatrix (f.symm ∘ v) := by ext;
   simp only [Basis.toMatrix_apply, Basis.map, LinearEquiv.trans_apply]
 #align basis.to_matrix_map Basis.toMatrix_map
 

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

@@ -68,30 +68,21 @@ variable (e : Basis ι R M) (v : ι' → M) (i : ι) (j : ι')
 namespace Basis
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_apply Basis.toMatrix_applyₓ'. -/
 theorem toMatrix_apply : e.toMatrix v i j = e.repr (v j) i :=
   rfl
 #align basis.to_matrix_apply Basis.toMatrix_apply
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_applyₓ'. -/
 theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
   funext fun _ => rfl
 #align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_apply
 
 /- warning: basis.to_matrix_eq_to_matrix_constr -> Basis.toMatrix_eq_toMatrix_constr is a dubious translation:
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_inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u3 u2, max (max u3 u2) u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) 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(Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u3 u2} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M 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(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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat 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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constrₓ'. -/
 theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M) :
     e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) :=
@@ -129,10 +120,7 @@ theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
 #align basis.to_matrix_self Basis.toMatrix_self
 
 /- warning: basis.to_matrix_update -> Basis.toMatrix_update is a dubious translation:
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-  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι') [_inst_7 : DecidableEq.{succ u4} ι'] (x : M), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (Matrix.{u3, u4, u2} ι ι' R) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (Function.update.{succ u4, succ u1} ι' (fun (ᾰ : ι') => M) (fun (a : ι') (b : ι') => _inst_7 a b) v j x)) (Matrix.updateColumn.{u2, u3, u4} ι ι' R (fun (a : ι') (b : ι') => _inst_7 a b) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun 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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_update Basis.toMatrix_updateₓ'. -/
 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) :=
@@ -200,10 +188,7 @@ theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b
 #align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMul
 
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_inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) 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_inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u4 u3) u2, u1, max (max (max u4 u3) u2) u1} R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u4 u3) u2, u1, max (max (max u4 u3) u2) u1} R R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max (max u4 u3) u2, u1} R R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Matrix.toLin.{u2, u4, u3, u1, u1} R _inst_1 ι ι' _inst_8 _inst_7 (fun (a : ι') (b : ι') => _inst_9 a b) M M _inst_2 _inst_2 _inst_3 _inst_3 v e) (Basis.toMatrix.{u4, u3, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι') => M) _x) (Basis.funLike.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) v))) (LinearMap.id.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_lin_to_matrix Basis.toLin_toMatrixₓ'. -/
 @[simp]
 theorem toLin_toMatrix [Fintype ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
@@ -257,10 +242,7 @@ section Fintype
 variable [Fintype ι'] [Fintype κ] [Fintype κ']
 
 /- warning: basis_to_matrix_mul_linear_map_to_matrix -> basis_toMatrix_mul_linearMap_toMatrix is a dubious translation:
-lean 3 declaration is
-  forall {ι' : Type.{u1}} {κ : Type.{u2}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u1, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u2, u4, u6} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u1} ι'] [_inst_10 : Fintype.{u2} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : 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-but is expected to have type
-  forall {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : 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(CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u6 u5) u4, max (max (max (max u6 u5) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u6 u5) u4, max (max (max (max u6 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u6 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (LinearMap.toMatrix.{u4, u5, u6, u1, u2} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_12 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul_linear_map_to_matrix basis_toMatrix_mul_linearMap_toMatrixₓ'. -/
 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
@@ -274,10 +256,7 @@ theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
 variable [Fintype ι]
 
 /- warning: linear_map_to_matrix_mul_basis_to_matrix -> linearMap_toMatrix_mul_basis_toMatrix is a dubious translation:
-lean 3 declaration is
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(CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 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(LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u4) u3} (Matrix.{u4, u6, u3} κ' ι R) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u3, max (max u6 u4) u3} R (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) 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_inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, max u2 u1, max (max u6 u4) u3} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearMap.toMatrix.{u3, u4, u6, u2, u1} R _inst_1 κ' ι _inst_12 _inst_11 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c') f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrixₓ'. -/
 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
@@ -287,10 +266,7 @@ theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι']
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
 
 /- warning: basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix -> basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ : Type.{u3}} {κ' : Type.{u4}} {R : Type.{u5}} {M : Type.{u6}} [_inst_1 : CommSemiring.{u5} R] [_inst_2 : AddCommMonoid.{u6} M] [_inst_3 : Module.{u5, u6} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2] {N : Type.{u7}} [_inst_7 : AddCommMonoid.{u7} N] [_inst_8 : Module.{u5, u7} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (b : Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u2, u5, u6} ι' R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (c : Basis.{u3, u5, u7} κ R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u3} κ] [_inst_11 : Fintype.{u4} κ'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'], Eq.{succ (max u3 u1 u5)} (Matrix.{u3, u1, u5} κ ι R) (Matrix.mul.{u5, u3, u2, u1} κ ι' ι R _inst_9 (Distrib.toHasMul.{u5} R (NonUnitalNonAssocSemiring.toDistrib.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.mul.{u5, u3, u4, u2} κ κ' ι' R _inst_11 (Distrib.toHasMul.{u5} R (NonUnitalNonAssocSemiring.toDistrib.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} 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(Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u6 u3) u4, max (max (max (max u6 u3) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) 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_inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrixₓ'. -/
 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c f := by
@@ -298,10 +274,7 @@ theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι
 #align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
 
 /- warning: basis_to_matrix_mul -> basis_toMatrix_mul is a dubious translation:
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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toZero.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toAddZeroClass.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u5 u6) u4) u3) u1, u4, max u3 u1, max (max u5 u6) u4} (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u3 u1, max (max u5 u6) u4, max (max (max (max u5 u6) u4) u3) u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u3 u1, max (max u5 u6) u4, max (max (max (max u5 u6) u4) u3) u1} R R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R 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_inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u2 u6) u4) u3) u1, u4, max (max u2 u6) u4, max u3 u1} (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} 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(AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul basis_toMatrix_mulₓ'. -/
 theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
@@ -311,10 +284,7 @@ theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis
 #align basis_to_matrix_mul basis_toMatrix_mul
 
 /- warning: mul_basis_to_matrix -> mul_basis_toMatrix is a dubious translation:
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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (SMulZeroClass.toSMul.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (AddMonoid.toZero.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (AddMonoid.toAddZeroClass.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u5 u2) u4) u3) u1, u4, max u3 u1, max (max u5 u2) u4} (LinearEquiv.{u4, u4, max u1 u3, max (max u4 u5) u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u3 u1, max (max u5 u2) u4, max (max (max (max u5 u2) u4) u3) u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (LinearEquiv.{u4, u4, max u1 u3, max (max u4 u5) u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N 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(LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 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(CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u2) u4} (Matrix.{u2, u6, u4} κ ι R) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u6 u2) u4} R (Matrix.{u2, u6, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u6 u2) u4, max u3 u1, max (max (max (max u6 u2) u4) u3) u1} R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u1 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align mul_basis_to_matrix mul_basis_toMatrixₓ'. -/
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
@@ -325,10 +295,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 #align mul_basis_to_matrix mul_basis_toMatrix
 
 /- warning: basis_to_matrix_basis_fun_mul -> basis_toMatrix_basisFun_mul is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (ι -> R) (AddMonoid.toZero.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (ι -> R) (AddMonoid.toAddZeroClass.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mulₓ'. -/
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
@@ -340,10 +307,7 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 
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(CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u1, u1} R R 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(RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrixₓ'. -/
 /-- A generalization of `linear_map.to_matrix_id`. -/
 @[simp]
@@ -355,10 +319,7 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
 #align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrix
 
 /- warning: basis.to_matrix_reindex' -> Basis.toMatrix_reindex' is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex' Basis.toMatrix_reindex'ₓ'. -/
 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
@@ -429,10 +390,7 @@ theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι
 #align basis.to_matrix_reindex Basis.toMatrix_reindex
 
 /- warning: basis.to_matrix_map -> Basis.toMatrix_map is a dubious translation:
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(SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} N _inst_7) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) f)) v))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map Basis.toMatrix_mapₓ'. -/
 @[simp]
 theorem Basis.toMatrix_map (b : Basis ι R M) (f : M ≃ₗ[R] N) (v : ι → N) :

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

@@ -71,7 +71,7 @@ namespace Basis
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (i : ι) (j : ι'), Eq.{succ u3} R (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R M _inst_1 _inst_2 _inst_3 e v i j) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (fun (_x : Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (coeFn.{max (succ u4) (succ (max u1 u3)), max (succ u4) (succ (max u1 u3))} (LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (fun (_x : LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) => M -> (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u3, u3, u4, max u1 u3} R R M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (Basis.repr.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) (v j)) i)
 but is expected to have type
-  forall {ι : Type.{u3}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] (e : Basis.{u3, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (i : ι) (j : ι'), Eq.{succ u4} R (Basis.toMatrix.{u3, u2, u4, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v i j) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), succ u1, max (succ u3) (succ u4)} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u1, u4, u1, max u3 u4} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SMulZeroClass.toSMul.{u4, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribSMul.toSMulZeroClass.{u4, u1} R M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribMulAction.toDistribSMul.{u4, u1} R M (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddMonoid.toZero.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u4, u1, max u3 u4} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u1, max u3 u4, max (max u3 u4) u1} R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u1, max u3 u4, max (max u3 u4) u1} R R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u1, max u3 u4} R R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (Basis.repr.{u3, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3 e) (v j)) i)
+  forall {ι : Type.{u3}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] (e : Basis.{u3, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (i : ι) (j : ι'), Eq.{succ u4} R (Basis.toMatrix.{u3, u2, u4, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v i j) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), succ u1, max (succ u3) (succ u4)} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u1, u4, u1, max u3 u4} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SMulZeroClass.toSMul.{u4, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribSMul.toSMulZeroClass.{u4, u1} R M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribMulAction.toDistribSMul.{u4, u1} R M (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddMonoid.toZero.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u4, u1, max u3 u4} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u4, max u3 u4} R (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u1, max u3 u4, max (max u3 u4) u1} R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u1, max u3 u4, max (max u3 u4) u1} R R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u1, max u3 u4} R R M (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (Basis.repr.{u3, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3 e) (v j)) i)
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_apply Basis.toMatrix_applyₓ'. -/
 theorem toMatrix_apply : e.toMatrix v i j = e.repr (v j) i :=
   rfl
@@ -81,7 +81,7 @@ theorem toMatrix_apply : e.toMatrix v i j = e.repr (v j) i :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι'), Eq.{max (succ u1) (succ u3)} (ι -> R) (Matrix.transpose.{u3, u1, u2} ι ι' R (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (fun (_x : Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (coeFn.{max (succ u4) (succ (max u1 u3)), max (succ u4) (succ (max u1 u3))} (LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (fun (_x : LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) => M -> (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u3, u3, u4, max u1 u3} R R M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (Basis.repr.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) (v j)))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u4, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι'), Eq.{max (succ u4) (succ u3)} (ι -> R) (Matrix.transpose.{u3, u4, u2} ι ι' R (Basis.toMatrix.{u4, u2, u3, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, max (succ u4) (succ u3)} (LinearEquiv.{u3, u3, 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u1, u3, u1, max u4 u3} (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u1} R M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribMulAction.toDistribSMul.{u3, u1} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddMonoid.toZero.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u1, u3, u1, max u4 u3} (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, max u4 u3, max (max u4 u3) u1} R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, max u4 u3, max (max u4 u3) u1} R R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, max u4 u3} R R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (Basis.repr.{u4, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) (v j)))
+  forall {ι : Type.{u4}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u4, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι'), Eq.{max (succ u4) (succ u3)} (ι -> R) (Matrix.transpose.{u3, u4, u2} ι ι' R (Basis.toMatrix.{u4, u2, u3, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, max (succ u4) (succ u3)} (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u1, u3, u1, max u4 u3} (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u1} R M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribMulAction.toDistribSMul.{u3, u1} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddMonoid.toZero.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u1, u3, u1, max u4 u3} (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, max u4 u3, max (max u4 u3) u1} R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, max u4 u3, max (max u4 u3) u1} R R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, max u4 u3} R R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (Basis.repr.{u4, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) (v j)))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_applyₓ'. -/
 theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
   funext fun _ => rfl
@@ -91,7 +91,7 @@ theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u1} ι] [_inst_8 : DecidableEq.{succ u1} ι] (v : ι -> M), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R M _inst_1 _inst_2 _inst_3 e v) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearEquiv.{u2, u2, u3, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.toMatrix._proof_1.{u2} R _inst_1) (LinearMap.toMatrix._proof_2.{u2} R _inst_1) (LinearMap.{u2, u2, u3, 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_inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u2, u3} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u2, u1, u1, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : LinearEquiv.{u2, u2, u3, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.toMatrix._proof_1.{u2} R _inst_1) (LinearMap.toMatrix._proof_2.{u2} R _inst_1) (LinearMap.{u2, u2, u3, u3} 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u1, u1, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u3, u3} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u1, u1} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.module.{u2, u2, u2, u3, u3} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u2, u3} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u2, u1, u1, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) => (LinearMap.{u2, u2, u3, u3} 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) -> (Matrix.{u1, u1, u2} ι ι R)) (LinearEquiv.hasCoeToFun.{u2, u2, u3, max u1 u2} R R (LinearMap.{u2, u2, u3, u3} 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u1, u1, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u3, u3} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u1, u1} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.module.{u2, u2, u2, u3, u3} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u2, u3} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u2, u1, u1, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.toMatrix._proof_1.{u2} R _inst_1) (LinearMap.toMatrix._proof_2.{u2} R _inst_1)) (LinearMap.toMatrix.{u2, u1, u1, u3, u3} R _inst_1 ι ι _inst_7 _inst_7 (fun (a : ι) (b : ι) => _inst_8 a b) M M _inst_2 _inst_2 _inst_3 _inst_3 e e) (coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (LinearEquiv.{0, 0, max u1 u3, u3} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} 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(Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u3, u3} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.Function.module.{u1, 0, u3} ι Nat M Nat.semiring _inst_2 (AddCommMonoid.natModule.{u3} M _inst_2)) (LinearMap.module.{u2, u2, 0, u3, u3} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) => (ι -> M) -> (LinearMap.{u2, u2, u3, u3} 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))) M M _inst_2 _inst_2 _inst_3 _inst_3)) (LinearEquiv.hasCoeToFun.{0, 0, max u1 u3, u3} Nat Nat (ι -> M) (LinearMap.{u2, u2, u3, u3} 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u1, u3} ι (fun (ᾰ : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u3, u3} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.Function.module.{u1, 0, u3} ι Nat M Nat.semiring _inst_2 (AddCommMonoid.natModule.{u3} M _inst_2)) (LinearMap.module.{u2, u2, 0, u3, u3} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)) (Basis.constr.{u1, u2, u3, u3, 0} ι R M M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 _inst_2 _inst_3 e Nat Nat.semiring (AddCommMonoid.natModule.{u3} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u3} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} M _inst_2) (Module.toDistribMulAction.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) v))
 but is expected to have type
-  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u3} ι] [_inst_8 : DecidableEq.{succ u3} ι] (v : ι -> M), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 e v) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (fun (_x : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => Matrix.{u3, u3, u2} ι ι R) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u3 u2, max (max u3 u2) u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u3 u2} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 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(CommSemiring.toSemiring.{u2} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat 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(LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max u3 u1} Nat (ι -> M) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2))) (Module.toDistribMulAction.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SemilinearMapClass.distribMulActionHomClass.{0, max u3 u1, u1, max u3 u1} Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max u3 u1, u1, max u3 u1} Nat Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max u3 u1, u1} Nat Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Basis.constr.{u3, u2, u1, u1, 0} ι R M M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 _inst_2 _inst_3 e Nat Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) v))
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u3} ι] [_inst_8 : DecidableEq.{succ u3} ι] (v : ι -> M), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 e v) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (fun (_x : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => Matrix.{u3, u3, u2} ι ι R) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 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(CommSemiring.toSemiring.{u2} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) _x) (SMulHomClass.toFunLike.{max u3 u1, 0, max u3 u1, u1} (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (SMulZeroClass.toSMul.{0, max u3 u1} Nat (ι -> M) (AddMonoid.toZero.{max u3 u1} (ι -> M) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)))) (DistribSMul.toSMulZeroClass.{0, max u3 u1} Nat (ι -> M) (AddMonoid.toAddZeroClass.{max u3 u1} (ι -> M) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)))) (DistribMulAction.toDistribSMul.{0, max u3 u1} Nat (ι -> M) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2))) (Module.toDistribMulAction.{0, max u3 u1} Nat (ι -> M) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, 0, max u3 u1, u1} (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max u3 u1} Nat (ι -> M) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2))) (Module.toDistribMulAction.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SemilinearMapClass.distribMulActionHomClass.{0, max u3 u1, u1, max u3 u1} Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max u3 u1, u1, max u3 u1} Nat Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{0, 0, max u3 u1, u1} Nat Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring)))))) (Basis.constr.{u3, u2, u1, u1, 0} ι R M M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 _inst_2 _inst_3 e Nat Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) v))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constrₓ'. -/
 theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M) :
     e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) :=
@@ -132,7 +132,7 @@ theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι') [_inst_7 : DecidableEq.{succ u2} ι'] (x : M), Eq.{succ (max u1 u2 u3)} (Matrix.{u1, u2, u3} ι ι' R) (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R M _inst_1 _inst_2 _inst_3 e (Function.update.{succ u2, succ u4} ι' (fun (ᾰ : ι') => M) (fun (a : ι') (b : ι') => _inst_7 a b) v j x)) (Matrix.updateColumn.{u3, u1, u2} ι ι' R (fun (a : ι') (b : ι') => _inst_7 a b) (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (fun (_x : Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (coeFn.{max (succ u4) (succ (max u1 u3)), max (succ u4) (succ (max u1 u3))} (LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (fun (_x : LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) => M -> (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u3, u3, u4, max u1 u3} R R M (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (Basis.repr.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) x)))
 but is expected to have type
-  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι') [_inst_7 : DecidableEq.{succ u4} ι'] (x : M), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (Matrix.{u3, u4, u2} ι ι' R) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (Function.update.{succ u4, succ u1} ι' (fun (ᾰ : ι') => M) (fun (a : ι') (b : ι') => _inst_7 a b) v j x)) (Matrix.updateColumn.{u2, u3, u4} ι ι' R (fun (a : ι') (b : ι') => _inst_7 a b) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribSMul.toSMulZeroClass.{u2, u1} R M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribMulAction.toDistribSMul.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u3 u2, max (max u3 u2) u1} R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u3 u2} R R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Basis.repr.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 e) x)))
+  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι') [_inst_7 : DecidableEq.{succ u4} ι'] (x : M), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (Matrix.{u3, u4, u2} ι ι' R) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (Function.update.{succ u4, succ u1} ι' (fun (ᾰ : ι') => M) (fun (a : ι') (b : ι') => _inst_7 a b) v j x)) (Matrix.updateColumn.{u2, u3, u4} ι ι' R (fun (a : ι') (b : ι') => _inst_7 a b) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R 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(Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SMulZeroClass.toSMul.{u2, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribSMul.toSMulZeroClass.{u2, u1} R M (AddMonoid.toAddZeroClass.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (DistribMulAction.toDistribSMul.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toZero.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u3 u2, max (max u3 u2) u1} R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u3 u2, max (max u3 u2) u1} R R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u3 u2} R R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Basis.repr.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 e) x)))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_update Basis.toMatrix_updateₓ'. -/
 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) :=
@@ -203,7 +203,7 @@ theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u1} ι] [_inst_8 : Fintype.{u2} ι'] [_inst_9 : DecidableEq.{succ u2} ι'] (v : Basis.{u2, u3, u4} ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3), Eq.{succ u4} (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (coeFn.{max (succ (max u1 u2 u3)) (succ u4), max (succ (max u1 u2 u3)) (succ u4)} (LinearEquiv.{u3, u3, max u1 u2 u3, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (Matrix.toLin._proof_1.{u3} R _inst_1) (Matrix.toLin._proof_2.{u3} R _inst_1) (Matrix.{u1, u2, u3} ι ι' R) (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u3, u1, u2} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.addCommMonoid.{u3, u3, u4, u4} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u4} ι] [_inst_8 : Fintype.{u3} ι'] [_inst_9 : DecidableEq.{succ u3} ι'] (v : Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u4, u3, u2} ι ι' R) => LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Basis.toMatrix.{u4, u3, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} 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ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (AddMonoid.toAddZeroClass.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max u4 u3) u2) u1, u2, max (max u4 u3) u2, u1} (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u4 u3) u2, u1, max (max (max u4 u3) u2) u1} R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) 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(CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max (max u4 u3) u2, u1} R R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Matrix.toLin.{u2, u4, u3, u1, u1} R _inst_1 ι ι' _inst_8 _inst_7 (fun (a : ι') (b : ι') => _inst_9 a b) M M _inst_2 _inst_2 _inst_3 _inst_3 v e) (Basis.toMatrix.{u4, u3, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι') => M) _x) (Basis.funLike.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) v))) (LinearMap.id.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u4} ι] [_inst_8 : Fintype.{u3} ι'] [_inst_9 : DecidableEq.{succ u3} ι'] (v : Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u4, u3, u2} ι ι' R) => LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Basis.toMatrix.{u4, u3, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} 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(CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (SMulZeroClass.toSMul.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (AddMonoid.toZero.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (AddMonoid.toAddZeroClass.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max u4 u3) u2) u1, u2, max (max u4 u3) u2, u1} (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u4 u3) u2, u1, max (max (max u4 u3) u2) u1} R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max (max u4 u3) u2, u1, max (max (max u4 u3) u2) u1} R R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max (max u4 u3) u2, u1} R R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Matrix.toLin.{u2, u4, u3, u1, u1} R _inst_1 ι ι' _inst_8 _inst_7 (fun (a : ι') (b : ι') => _inst_9 a b) M M _inst_2 _inst_2 _inst_3 _inst_3 v e) (Basis.toMatrix.{u4, u3, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι') => M) _x) (Basis.funLike.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) v))) (LinearMap.id.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)
 Case conversion may be inaccurate. Consider using '#align basis.to_lin_to_matrix Basis.toLin_toMatrixₓ'. -/
 @[simp]
 theorem toLin_toMatrix [Fintype ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
@@ -260,7 +260,7 @@ variable [Fintype ι'] [Fintype κ] [Fintype κ']
 lean 3 declaration is
   forall {ι' : Type.{u1}} {κ : Type.{u2}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u1, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u2, u4, u6} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u1} ι'] [_inst_10 : Fintype.{u2} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : DecidableEq.{succ u1} ι'], Eq.{succ (max u2 u1 u4)} (Matrix.{u2, u1, u4} κ ι' R) (Matrix.mul.{u4, u2, u3, u1} κ κ' ι' R _inst_11 (Distrib.toHasMul.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Basis.toMatrix.{u2, u3, u4, u6} κ κ' R N _inst_1 _inst_7 _inst_8 c (coeFn.{max (succ u3) (succ u4) (succ u6), max (succ u3) (succ u6)} (Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (fun (_x : Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) => κ' -> N) (FunLike.hasCoeToFun.{max (succ u3) (succ u4) (succ u6), succ u3, succ u6} (Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) κ' (fun (_x : κ') => N) (Basis.funLike.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)) c')) (coeFn.{max (succ (max u5 u6)) (succ (max u3 u1 u4)), max (succ (max u5 u6)) (succ (max u3 u1 u4))} (LinearEquiv.{u4, u4, max u5 u6, max u3 u1 u4} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1) (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u1} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u3, u1, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (fun (_x : LinearEquiv.{u4, u4, max u5 u6, max u3 u1 u4} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1) (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u1} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u3, u1, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u1, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u2, u1} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u2, u1, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) => (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u2, u1, u4} κ ι' R)) (LinearEquiv.hasCoeToFun.{u4, u4, max u5 u6, max u2 u1 u4} R R (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u1, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u2, u1} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u2, u1, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1)) (LinearMap.toMatrix.{u4, u2, u1, u5, u6} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_12 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c) f)
 but is expected to have type
-  forall {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : DecidableEq.{succ u6} ι'], Eq.{max (max (succ u6) (succ u5)) (succ u4)} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.mul.{u4, u5, u3, u6} κ κ' ι' R _inst_11 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Basis.toMatrix.{u5, u3, u4, u2} κ κ' R N _inst_1 _inst_7 _inst_8 c (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), succ u3, succ u2} (Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) κ' (fun (_x : κ') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ') => N) _x) (Basis.funLike.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) c')) (FunLike.coe.{max (max (max (max (succ u6) (succ u3)) (succ u4)) (succ u1)) (succ u2), 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_inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (fun (_x : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, 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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 u3) u4) u1) u2, u4, max u1 u2, max (max u6 u3) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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(smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (SMulZeroClass.toSMul.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (AddMonoid.toZero.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (AddMonoid.toAddZeroClass.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 u5) u4) u1) u2, u4, max u1 u2, max (max u6 u5) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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(AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u6 u5) u4, max (max (max (max u6 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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_inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u6 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (LinearMap.toMatrix.{u4, u5, u6, u1, u2} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_12 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c) f)
+  forall {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : DecidableEq.{succ u6} ι'], Eq.{max (max (succ u6) (succ u5)) (succ u4)} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.mul.{u4, u5, u3, u6} κ κ' ι' R _inst_11 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Basis.toMatrix.{u5, u3, u4, u2} κ κ' R N _inst_1 _inst_7 _inst_8 c (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), succ u3, succ u2} (Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) κ' (fun (_x : κ') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ') => N) _x) (Basis.funLike.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) c')) (FunLike.coe.{max (max (max (max (succ u6) (succ u3)) (succ u4)) (succ u1)) (succ u2), 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(CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 u3) u4) u1) u2, u4, max u1 u2, max (max u6 u3) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) => Matrix.{u5, u6, u4} κ ι' R) _x) (SMulHomClass.toFunLike.{max (max (max (max u6 u5) u4) u1) u2, u4, max u1 u2, max (max u6 u5) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, 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(AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u5) u4} (Matrix.{u5, u6, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 u5) u4) u1) u2, u4, max u1 u2, max (max u6 u5) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u5) u4} R (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u6 u5) u4, max (max (max (max u6 u5) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u6 u5) u4, max (max (max (max u6 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u6 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (LinearMap.toMatrix.{u4, u5, u6, u1, u2} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_12 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c) f)
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul_linear_map_to_matrix basis_toMatrix_mul_linearMap_toMatrixₓ'. -/
 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
@@ -277,7 +277,7 @@ variable [Fintype ι]
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b : Basis.{u1, u4, u5} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c' : Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u2} ι'] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'], Eq.{succ (max u3 u1 u4)} (Matrix.{u3, u1, u4} κ' ι R) (Matrix.mul.{u4, u3, u2, u1} κ' ι' ι R _inst_9 (Distrib.toHasMul.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (coeFn.{max (succ (max u5 u6)) (succ (max u3 u2 u4)), max (succ (max u5 u6)) (succ (max u3 u2 u4))} (LinearEquiv.{u4, u4, max u5 u6, max u3 u2 u4} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1) (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u2, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u2} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u4} κ' ι R) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u1} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u3, u1, u4} κ' ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) => (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u3, u1, u4} κ' ι R)) (LinearEquiv.hasCoeToFun.{u4, u4, max u5 u6, max u3 u1 u4} R R (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u4} κ' ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u1} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u3, u1, u4} κ' ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1)) (LinearMap.toMatrix.{u4, u3, u1, u5, u6} R _inst_1 κ' ι _inst_12 _inst_11 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c') f)
 but is expected to have type
-  forall {ι : Type.{u6}} {ι' : Type.{u5}} {κ' : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7] (b : Basis.{u6, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u5, u3, u2} ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (c' : Basis.{u4, u3, u1} κ' R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u5} ι'] [_inst_11 : Fintype.{u4} κ'] [_inst_12 : Fintype.{u6} ι] [_inst_13 : 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(LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u4) u3} (Matrix.{u4, u6, u3} κ' ι R) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u3, max (max u6 u4) u3} R (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, max u2 u1, max (max u6 u4) u3} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearMap.toMatrix.{u3, u4, u6, u2, u1} R _inst_1 κ' ι _inst_12 _inst_11 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c') f)
+  forall {ι : Type.{u6}} {ι' : Type.{u5}} {κ' : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7] (b : Basis.{u6, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u5, u3, u2} ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (c' : Basis.{u4, u3, u1} κ' R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u5} ι'] [_inst_11 : Fintype.{u4} κ'] [_inst_12 : Fintype.{u6} ι] [_inst_13 : DecidableEq.{succ u6} ι] [_inst_14 : DecidableEq.{succ u5} ι'], Eq.{max (max (succ u6) (succ u4)) (succ u3)} (Matrix.{u4, u6, u3} κ' ι R) (Matrix.mul.{u3, u4, u5, u6} κ' ι' ι R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (FunLike.coe.{max (max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)) (succ u1), max (succ u2) (succ u1), max (max (succ u5) (succ u4)) (succ u3)} (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u5) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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(Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u4) u3} (Matrix.{u4, u5, u3} κ' ι' R) (Matrix.addCommMonoid.{u3, u4, u5} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u1} R (LinearMap.{u3, u3, 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(LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u4) u3} (Matrix.{u4, u6, u3} κ' ι R) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u3, max (max u6 u4) u3} R (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) 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_inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, max u2 u1, max (max u6 u4) u3} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearMap.toMatrix.{u3, u4, u6, u2, u1} R _inst_1 κ' ι _inst_12 _inst_11 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c') f)
 Case conversion may be inaccurate. Consider using '#align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrixₓ'. -/
 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
@@ -290,7 +290,7 @@ theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι']
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ : Type.{u3}} {κ' : Type.{u4}} {R : Type.{u5}} {M : Type.{u6}} [_inst_1 : CommSemiring.{u5} R] [_inst_2 : AddCommMonoid.{u6} M] [_inst_3 : Module.{u5, u6} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2] {N : Type.{u7}} [_inst_7 : AddCommMonoid.{u7} N] [_inst_8 : Module.{u5, u7} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (b : Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u2, u5, u6} ι' R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (c : Basis.{u3, u5, u7} κ R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u3} κ] [_inst_11 : Fintype.{u4} κ'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'], Eq.{succ (max u3 u1 u5)} (Matrix.{u3, u1, u5} κ ι R) (Matrix.mul.{u5, u3, u2, u1} κ ι' ι R _inst_9 (Distrib.toHasMul.{u5} R (NonUnitalNonAssocSemiring.toDistrib.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.mul.{u5, u3, u4, u2} κ κ' ι' R _inst_11 (Distrib.toHasMul.{u5} R (NonUnitalNonAssocSemiring.toDistrib.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Basis.toMatrix.{u3, u4, u5, u7} κ κ' R N _inst_1 _inst_7 _inst_8 c (coeFn.{max (succ u4) (succ u5) (succ u7), max (succ u4) (succ u7)} (Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (fun (_x : Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) => κ' -> N) (FunLike.hasCoeToFun.{max (succ u4) (succ u5) (succ u7), succ u4, succ u7} (Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) κ' (fun (_x : κ') => N) (Basis.funLike.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8)) c')) (coeFn.{max (succ (max u6 u7)) (succ (max u4 u2 u5)), max (succ (max u6 u7)) (succ (max u4 u2 u5))} (LinearEquiv.{u5, u5, max u6 u7, max u4 u2 u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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(CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u4, u2, u5} κ' ι' R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (fun (_x : LinearEquiv.{u5, u5, max u6 u7, max u4 u2 u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (LinearMap.toMatrix._proof_1.{u5} R _inst_1) (LinearMap.toMatrix._proof_2.{u5} R _inst_1) (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u2, u5} κ' ι' R) (LinearMap.addCommMonoid.{u5, u5, u6, u7} R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.addCommMonoid.{u5, u4, u2} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u4, u2, u5} κ' ι' R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) => (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u4, u2, u5} κ' ι' R)) (LinearEquiv.hasCoeToFun.{u5, u5, max u6 u7, max u4 u2 u5} R R (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u2, u5} κ' ι' R) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (LinearMap.addCommMonoid.{u5, u5, u6, u7} R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.addCommMonoid.{u5, u4, u2} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u4, u2, u5} κ' ι' R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (LinearMap.toMatrix._proof_1.{u5} R _inst_1) (LinearMap.toMatrix._proof_2.{u5} R _inst_1)) (LinearMap.toMatrix.{u5, u4, u2, u6, u7} R _inst_1 κ' ι' _inst_9 _inst_11 (fun (a : ι') (b : ι') => _inst_14 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c') f)) (Basis.toMatrix.{u2, u1, u5, u6} ι' ι R M _inst_1 _inst_2 _inst_3 b' (coeFn.{max (succ u1) (succ u5) (succ u6), max (succ u1) (succ u6)} (Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u1) (succ u5) (succ u6), succ u1, succ u6} (Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3)) b))) (coeFn.{max (succ (max u6 u7)) (succ (max u3 u1 u5)), max (succ (max u6 u7)) (succ (max u3 u1 u5))} (LinearEquiv.{u5, u5, max u6 u7, max u3 u1 u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R 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_inst_1))) (LinearMap.toMatrix._proof_1.{u5} R _inst_1) (LinearMap.toMatrix._proof_2.{u5} R _inst_1) (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u5} κ ι R) (LinearMap.addCommMonoid.{u5, u5, u6, u7} R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.addCommMonoid.{u5, u3, u1} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u3, u1, u5} κ ι R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) => (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u3, u1, u5} κ ι R)) (LinearEquiv.hasCoeToFun.{u5, u5, max u6 u7, max u3 u1 u5} R R (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u5} κ ι R) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (LinearMap.addCommMonoid.{u5, u5, u6, u7} R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.addCommMonoid.{u5, u3, u1} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u3, u1, u5} κ ι R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (LinearMap.toMatrix._proof_1.{u5} R _inst_1) (LinearMap.toMatrix._proof_2.{u5} R _inst_1)) (LinearMap.toMatrix.{u5, u3, u1, u6, u7} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c) f)
 but is expected to have type
-  forall {ι : Type.{u7}} {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b : Basis.{u7, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : Fintype.{u7} ι] [_inst_13 : DecidableEq.{succ u7} ι] [_inst_14 : DecidableEq.{succ u6} ι'], Eq.{max (max (succ u7) (succ u5)) (succ u4)} (Matrix.{u5, u7, u4} κ ι R) (Matrix.mul.{u4, u5, u6, u7} κ ι' ι R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.mul.{u4, u5, u3, u6} κ κ' ι' R _inst_11 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Basis.toMatrix.{u5, u3, u4, u2} κ κ' R N _inst_1 _inst_7 _inst_8 c (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u2), succ u3, succ u2} (Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) κ' (fun (_x : κ') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : κ') => N) _x) (Basis.funLike.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) c')) (FunLike.coe.{max (max (max (max (succ u6) (succ u3)) (succ u4)) (succ u1)) (succ u2), max (succ u1) (succ u2), max (max (succ u6) (succ u3)) (succ u4)} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (fun (_x : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) => Matrix.{u3, u6, u4} κ' ι' R) _x) (SMulHomClass.toFunLike.{max (max (max (max u6 u3) u4) u1) u2, u4, max u1 u2, max (max u6 u3) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (SMulZeroClass.toSMul.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddMonoid.toZero.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (SMulZeroClass.toSMul.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (AddMonoid.toZero.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (AddMonoid.toAddZeroClass.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 u3) u4) u1) u2, u4, max u1 u2, max (max u6 u3) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u6 u3) u4, max (max (max (max u6 u3) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u6 u3) u4, max (max (max (max u6 u3) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) 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(CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (SMulZeroClass.toSMul.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (AddMonoid.toZero.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (AddCommMonoid.toAddMonoid.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (AddMonoid.toAddZeroClass.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (AddCommMonoid.toAddMonoid.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u7 u5) u4) u1) u2, u4, max u1 u2, max (max u7 u5) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) 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_inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u7 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (LinearMap.toMatrix.{u4, u5, u7, u1, u2} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c) f)
+  forall {ι : Type.{u7}} {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b : Basis.{u7, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : Fintype.{u7} ι] [_inst_13 : DecidableEq.{succ u7} ι] [_inst_14 : DecidableEq.{succ u6} ι'], Eq.{max (max (succ u7) (succ u5)) (succ u4)} (Matrix.{u5, u7, u4} κ ι R) (Matrix.mul.{u4, u5, u6, u7} κ ι' ι R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.mul.{u4, u5, u3, u6} κ κ' ι' R _inst_11 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddMonoid.toAddZeroClass.{max u1 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (SMulZeroClass.toSMul.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (AddMonoid.toZero.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (AddMonoid.toAddZeroClass.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 u3) u4) u1) u2, u4, max u1 u2, max (max u6 u3) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} 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(Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u6 u3) u4, max (max (max (max u6 u3) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} 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_inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddMonoid.toAddZeroClass.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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(Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u7 u5) u4) u1) u2, u4, max u1 u2, max (max u7 u5) u4} (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R 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(Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u7 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (LinearMap.toMatrix.{u4, u5, u7, u1, u2} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c) f)
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrixₓ'. -/
 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c f := by
@@ -301,7 +301,7 @@ theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u3} κ] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u3} κ] (b₁ : Basis.{u1, u4, u5} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u3, u4, u6} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u3, u4} ι' κ R), Eq.{succ (max u1 u3 u4)} (Matrix.{u1, u3, u4} ι κ R) (Matrix.mul.{u4, u1, u2, u3} ι ι' κ R _inst_9 (Distrib.toHasMul.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Basis.toMatrix.{u1, u2, u4, u5} ι ι' R M _inst_1 _inst_2 _inst_3 b₁ (coeFn.{max (succ u2) (succ u4) (succ u5), max (succ u2) (succ u5)} (Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) => ι' -> M) (FunLike.hasCoeToFun.{max (succ u2) (succ u4) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => M) (Basis.funLike.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)) b₂)) A) (coeFn.{max (succ (max u6 u5)) (succ (max u1 u3 u4)), max (succ (max 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(Matrix.addCommMonoid.{u4, u1, u3} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u4, u1, u3, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (fun (_x : LinearEquiv.{u4, u4, max u6 u5, max u1 u3 u4} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1) (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u1, u3, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u6, u5} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u1, u3} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u4, u1, u3, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) => (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) -> (Matrix.{u1, u3, u4} ι κ R)) (LinearEquiv.hasCoeToFun.{u4, u4, max u6 u5, max u1 u3 u4} R R (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u1, u3, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u6, u5} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u1, u3} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u4, u1, u3, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1)) (LinearMap.toMatrix.{u4, u1, u3, u6, u5} R _inst_1 ι κ _inst_10 _inst_12 (fun (a : κ) (b : κ) => _inst_13 a b) N M _inst_7 _inst_2 _inst_8 _inst_3 b₃ b₁) (coeFn.{max (succ (max u2 u3 u4)) (succ (max u6 u5)), max (succ (max u2 u3 u4)) (succ (max u6 u5))} (LinearEquiv.{u4, u4, max u2 u3 u4, max u6 u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1) (Matrix.{u2, u3, u4} ι' κ R) (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u3} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u6, u5} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u3, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (Matrix.toLin._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3))) (fun (_x : LinearEquiv.{u4, u4, max u2 u3 u4, max u6 u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1) (Matrix.{u2, u3, u4} ι' κ R) (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u3} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u6, u5} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u3, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (Matrix.toLin._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3))) => (Matrix.{u2, u3, u4} ι' κ R) -> (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3)) (LinearEquiv.hasCoeToFun.{u4, u4, max u2 u3 u4, max u6 u5} R R (Matrix.{u2, u3, u4} ι' κ R) (LinearMap.{u4, u4, u6, u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u3} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u6, u5} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u3, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (Matrix.toLin._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1)) (Matrix.toLin.{u4, u2, u3, u6, u5} R _inst_1 ι' κ _inst_10 _inst_9 (fun (a : κ) (b : κ) => _inst_13 a b) N M _inst_7 _inst_2 _inst_8 _inst_3 b₃ b₂) A))
 but is expected to have type
-  forall {ι : Type.{u5}} {ι' : Type.{u2}} {κ : Type.{u6}} {R : Type.{u4}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u6} κ] [_inst_12 : Fintype.{u5} ι] [_inst_13 : DecidableEq.{succ u6} κ] (b₁ : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u2, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u6, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u6, u4} ι' κ R), Eq.{max (max (succ u5) (succ u6)) (succ u4)} (Matrix.{u5, u6, u4} ι κ R) (Matrix.mul.{u4, u5, u2, u6} ι ι' κ R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Basis.toMatrix.{u5, u2, u4, u3} ι ι' R M _inst_1 _inst_2 _inst_3 b₁ (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u3), succ u2, succ u3} (Basis.{u2, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι') => M) _x) (Basis.funLike.{u2, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) b₂)) A) (FunLike.coe.{max (max (max (max (succ u5) (succ u6)) (succ u4)) (succ u3)) (succ u1), max (succ u3) (succ u1), max (max (succ u5) (succ u6)) (succ u4)} (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (fun (_x : LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) => Matrix.{u5, u6, u4} ι κ R) _x) (SMulHomClass.toFunLike.{max (max (max (max u5 u6) u4) u3) u1, u4, max u3 u1, max (max u5 u6) u4} (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (SMulZeroClass.toSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toZero.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toZero.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toAddZeroClass.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u5 u6) u4) u3) u1, u4, max u3 u1, max (max u5 u6) u4} (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) 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_inst_7 _inst_2 _inst_8 _inst_3) (SMulZeroClass.toSMul.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (AddMonoid.toZero.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (AddMonoid.toAddZeroClass.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toZero.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u2 u6) u4) u3) u1, u4, max (max u2 u6) u4, max u3 u1} (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} 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(Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max (max u2 u6) u4, max u3 u1} R R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R 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+  forall {ι : Type.{u5}} {ι' : Type.{u2}} {κ : Type.{u6}} {R : Type.{u4}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u6} κ] [_inst_12 : Fintype.{u5} ι] [_inst_13 : DecidableEq.{succ u6} κ] (b₁ : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u2, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u6, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u6, u4} ι' κ R), Eq.{max (max (succ u5) (succ u6)) (succ u4)} (Matrix.{u5, u6, u4} ι κ R) (Matrix.mul.{u4, u5, u2, u6} ι ι' κ R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (fun (_x : LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) => Matrix.{u5, u6, u4} ι κ R) _x) 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_inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (SMulZeroClass.toSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toZero.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toZero.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toAddZeroClass.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u5 u6) u4) u3) u1, u4, max u3 u1, max (max u5 u6) u4} (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 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(CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (SMulZeroClass.toSMul.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (AddMonoid.toZero.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (AddMonoid.toAddZeroClass.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (SMulZeroClass.toSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toZero.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u2 u6) u4) u3) u1, u4, max (max u2 u6) u4, max u3 u1} (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} 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(Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max (max u2 u6) u4, max u3 u1} R R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (Matrix.toLin.{u4, u2, u6, u1, u3} R _inst_1 ι' κ _inst_10 _inst_9 (fun (a : κ) (b : κ) => _inst_13 a b) N M _inst_7 _inst_2 _inst_8 _inst_3 b₃ b₂) A))
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul basis_toMatrix_mulₓ'. -/
 theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
@@ -314,7 +314,7 @@ theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u3} κ] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'] (b₁ : Basis.{u1, u4, u5} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u3, u4, u6} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u3, u1, u4} κ ι R), Eq.{succ (max u3 u2 u4)} (Matrix.{u3, u2, u4} κ ι' R) (Matrix.mul.{u4, u3, u1, u2} κ ι ι' R _inst_12 (Distrib.toHasMul.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) A (Basis.toMatrix.{u1, u2, u4, u5} ι ι' R M _inst_1 _inst_2 _inst_3 b₁ (coeFn.{max (succ u2) (succ u4) (succ u5), max (succ u2) (succ u5)} (Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) => ι' -> M) (FunLike.hasCoeToFun.{max (succ u2) (succ u4) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => M) (Basis.funLike.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)) b₂))) (coeFn.{max (succ (max u5 u6)) (succ (max u3 u2 u4)), max (succ (max 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u3, u2, u4} κ ι' R)) (LinearEquiv.hasCoeToFun.{u4, u4, max u5 u6, max u3 u2 u4} R R (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u2, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u2} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u3, u2, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1)) (LinearMap.toMatrix.{u4, u3, u2, u5, u6} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_14 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b₂ b₃) (coeFn.{max (succ (max u3 u1 u4)) (succ (max u5 u6)), max (succ (max u3 u1 u4)) (succ (max u5 u6))} (LinearEquiv.{u4, u4, max u3 u1 u4, max u5 u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1) (Matrix.{u3, u1, u4} κ ι R) (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.addCommMonoid.{u4, u3, u1} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u3, u1, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (Matrix.toLin._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8))) (fun (_x : LinearEquiv.{u4, u4, max u3 u1 u4, max u5 u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1) (Matrix.{u3, u1, u4} κ ι R) (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.addCommMonoid.{u4, u3, u1} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u3, u1, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (Matrix.toLin._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8))) => (Matrix.{u3, u1, u4} κ ι R) -> (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8)) (LinearEquiv.hasCoeToFun.{u4, u4, max u3 u1 u4, max u5 u6} R R (Matrix.{u3, u1, u4} κ ι R) (LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u1} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u3, u1, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (Matrix.toLin._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1)) (Matrix.toLin.{u4, u3, u1, u5, u6} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b₁ b₃) A))
 but is expected to have type
-  forall {ι : Type.{u6}} {ι' : Type.{u5}} {κ : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u5} ι'] [_inst_10 : Fintype.{u2} κ] [_inst_12 : Fintype.{u6} ι] [_inst_13 : DecidableEq.{succ u6} ι] [_inst_14 : DecidableEq.{succ u5} ι'] (b₁ : Basis.{u6, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u5, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u6, u4} κ ι R), Eq.{max (max (succ u5) (succ u2)) (succ u4)} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.mul.{u4, u2, u6, u5} κ ι ι' R _inst_12 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) A (Basis.toMatrix.{u6, u5, u4, u3} ι ι' R M _inst_1 _inst_2 _inst_3 b₁ (FunLike.coe.{max (max (succ u5) (succ u4)) (succ u3), succ u5, succ u3} (Basis.{u5, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) ι' (fun (_x : ι') => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι') => M) _x) (Basis.funLike.{u5, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) b₂))) (FunLike.coe.{max (max (max (max (succ u5) (succ u2)) (succ u4)) (succ u3)) (succ u1), max (succ u3) (succ u1), max (max (succ u5) (succ u2)) (succ u4)} (LinearEquiv.{u4, u4, max u1 u3, max (max u4 u5) u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 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(smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u2) u4} (Matrix.{u2, u6, u4} κ ι R) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max (max u6 u2) u4, max u3 u1, max (max 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N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max (max u6 u2) u4, max u3 u1} R R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (Matrix.toLin.{u4, u2, u6, u3, u1} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b₁ b₃) A))
+  forall {ι : Type.{u6}} {ι' : Type.{u5}} {κ : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u5} ι'] [_inst_10 : Fintype.{u2} κ] [_inst_12 : Fintype.{u6} ι] [_inst_13 : DecidableEq.{succ u6} ι] [_inst_14 : DecidableEq.{succ u5} ι'] (b₁ : Basis.{u6, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u5, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u6, u4} κ ι R), Eq.{max (max (succ u5) (succ u2)) (succ u4)} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.mul.{u4, u2, u6, u5} κ ι ι' R _inst_12 (NonUnitalNonAssocSemiring.toMul.{u4} R 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(smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u2) u4} (Matrix.{u2, u6, u4} κ ι R) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u6 u2) u4} R (Matrix.{u2, u6, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u6 u2) u4, max u3 u1, max (max (max (max u6 u2) u4) u3) u1} R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u1 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max (max u6 u2) u4, max u3 u1, max (max (max (max u6 u2) u4) u3) u1} R R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u1 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max (max u6 u2) u4, max u3 u1} R R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (Matrix.toLin.{u4, u2, u6, u3, u1} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b₁ b₃) A))
 Case conversion may be inaccurate. Consider using '#align mul_basis_to_matrix mul_basis_toMatrixₓ'. -/
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
@@ -328,7 +328,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{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)))) (Basis.toMatrix.{u1, u1, u2, max u1 u2} ι ι R (ι -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) b (coeFn.{max (succ u1) (succ u2) (succ 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 but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b) (Matrix.transpose.{u1, u2, u2} ι ι R A j)) i))
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mulₓ'. -/
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
@@ -343,7 +343,7 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (b : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u2, u3, u4} ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) [_inst_9 : Fintype.{u2} ι'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι], Eq.{succ (max u2 u1 u3)} (Matrix.{u2, u1, u3} ι' ι R) (coeFn.{max (succ u4) (succ (max u2 u1 u3)), max (succ u4) (succ (max u2 u1 u3))} (LinearEquiv.{u3, u3, u4, max u2 u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (LinearMap.toMatrix._proof_1.{u3} R _inst_1) (LinearMap.toMatrix._proof_2.{u3} R _inst_1) (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u2, u1, u3} ι' ι R) (LinearMap.addCommMonoid.{u3, u3, u4, u4} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u2, u1} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.module.{u3, u3, u3, u4, u4} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u3, u4} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u3, u2, u1, u3} ι' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (fun (_x : LinearEquiv.{u3, u3, u4, max u2 u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (LinearMap.toMatrix._proof_1.{u3} R _inst_1) (LinearMap.toMatrix._proof_2.{u3} R _inst_1) (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u2, u1, u3} ι' ι R) (LinearMap.addCommMonoid.{u3, u3, u4, u4} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u2, u1} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.module.{u3, u3, u3, u4, u4} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u3, u4} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u3, u2, u1, u3} ι' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) => (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) -> (Matrix.{u2, u1, u3} ι' ι R)) (LinearEquiv.hasCoeToFun.{u3, u3, u4, max u2 u1 u3} R R (LinearMap.{u3, u3, u4, u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u2, u1, u3} ι' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u4, u4} R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u2, u1} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.module.{u3, u3, u3, u4, u4} R R R M M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 (LinearMap.toMatrix._proof_3.{u3, u4} R _inst_1 M _inst_2 _inst_3)) (Matrix.module.{u3, u2, u1, u3} ι' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (LinearMap.toMatrix._proof_1.{u3} R _inst_1) (LinearMap.toMatrix._proof_2.{u3} R _inst_1)) (LinearMap.toMatrix.{u3, u2, u1, u4, u4} R _inst_1 ι' ι _inst_12 _inst_9 (fun (a : ι) (b : ι) => _inst_13 a b) M M _inst_2 _inst_2 _inst_3 _inst_3 b b') (LinearMap.id.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)) (Basis.toMatrix.{u2, u1, u3, u4} ι' ι R M _inst_1 _inst_2 _inst_3 b' (coeFn.{max (succ u1) (succ u3) (succ u4), max (succ u1) (succ u4)} (Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u1) (succ u3) (succ u4), succ u1, succ u4} (Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)) b))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι], Eq.{max (max (succ u4) (succ u3)) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => Matrix.{u3, u4, u2} ι' ι R) (LinearMap.id.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)) (FunLike.coe.{max (max (max (succ u4) 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_inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (fun (_x : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R 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_inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R 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R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u2, max (max u4 u3) u2} R (Matrix.{u3, u4, u2} ι' ι R) (AddMonoid.toZero.{max (max u4 u3) u2} (Matrix.{u3, u4, u2} ι' ι R) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u3, u4, u2} ι' ι R) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max (max u4 u3) u2} R (Matrix.{u3, u4, u2} ι' ι R) (AddMonoid.toAddZeroClass.{max (max u4 u3) u2} (Matrix.{u3, u4, u2} ι' ι R) (AddCommMonoid.toAddMonoid.{max (max u4 u3) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max u4 u3) u2) u1, u2, u1, max (max u4 u3) u2} (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u3, u4, u2} ι' ι R) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u3, u4, u2} ι' ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R 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+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u3, u2, u1} ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι], Eq.{max (max (succ u4) (succ u3)) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) => Matrix.{u3, u4, u2} ι' ι R) (LinearMap.id.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)) (FunLike.coe.{max (max (max (succ u4) 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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} 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u2} (Matrix.{u3, u4, u2} ι' ι R) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max (max u4 u3) u2} R (Matrix.{u3, u4, u2} ι' ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u3, u4, u2} ι' ι R) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u3, u4, u2} ι' ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max u4 u3) u2) u1, u2, u1, max (max u4 u3) u2} (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u3, u4, u2} ι' ι R) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u3, u4, u2} ι' ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max (max u4 u3) u2} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (LinearMap.toMatrix.{u2, u3, u4, u1, u1} R _inst_1 ι' ι _inst_12 _inst_9 (fun (a : ι) (b : ι) => _inst_13 a b) M M _inst_2 _inst_2 _inst_3 _inst_3 b b') (LinearMap.id.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)) (Basis.toMatrix.{u3, u4, u2, u1} ι' ι R M _inst_1 _inst_2 _inst_3 b' (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), succ u4, succ u1} (Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) b))
 Case conversion may be inaccurate. Consider using '#align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrixₓ'. -/
 /-- A generalization of `linear_map.to_matrix_id`. -/
 @[simp]
@@ -358,7 +358,7 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] [_inst_9 : Fintype.{u2} ι'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'] (b : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u1, succ u2} ι ι'), Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} ι' ι' R) (Basis.toMatrix.{u2, u2, u3, u4} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u1, u2, u3, u4} ι ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 b e) v) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgEquiv.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgEquiv.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) => (Matrix.{u1, u1, u3} ι ι R) -> (Matrix.{u2, u2, u3} ι' ι' R)) (AlgEquiv.hasCoeToFun.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) (Matrix.reindexAlgEquiv.{u1, u2, u3} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u1, u1, u3, u4} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u1, succ u2, succ u4} ι ι' M v (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e))))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι] [_inst_14 : DecidableEq.{succ u3} ι'] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u3} ι ι'), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι' ι' R) (Basis.toMatrix.{u3, u3, u2, u1} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u3, u2, u1} ι ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 b e) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Matrix.{u4, u4, u2} ι ι R) (fun (_x : Matrix.{u4, u4, u2} ι ι R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u4, u4, u2} ι ι R) => Matrix.{u3, u3, u2} ι' ι' R) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (SMulZeroClass.toSMul.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (AddMonoid.toZero.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))))) 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(Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u4 u2, max u3 u2, max (max u4 u3) u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u4 u2, max u3 u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (Matrix.reindexAlgEquiv.{u4, u3, u2} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u4, u4, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u4, succ u3, succ u1} ι ι' M v (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e))))
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι] [_inst_14 : DecidableEq.{succ u3} ι'] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u3} ι ι'), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι' ι' R) (Basis.toMatrix.{u3, u3, u2, u1} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u3, u2, u1} ι ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 b e) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R 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(Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))))) 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(Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) 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(Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u4 u2, max u3 u2, max (max u4 u3) u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u4 u2, max u3 u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (Matrix.reindexAlgEquiv.{u4, u3, u2} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u4, u4, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u4, succ u3, succ u1} ι ι' M v (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e))))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex' Basis.toMatrix_reindex'ₓ'. -/
 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
@@ -432,7 +432,7 @@ theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {N : Type.{u4}} [_inst_7 : AddCommMonoid.{u4} N] [_inst_8 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7] (b : Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (f : LinearEquiv.{u2, u2, u3, u4} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M N _inst_2 _inst_7 _inst_3 _inst_8) (v : ι -> N), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R) (Basis.toMatrix.{u1, u1, u2, u4} ι ι R N _inst_1 _inst_7 _inst_8 (Basis.map.{u1, u2, u3, u4} ι R M N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 _inst_7 _inst_8 b f) v) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u1, succ u4, succ u3} ι N M (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (LinearEquiv.{u2, u2, u4, u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (fun (_x : LinearEquiv.{u2, u2, u4, u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) => N -> M) (LinearEquiv.hasCoeToFun.{u2, u2, u4, u3} R R N M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearEquiv.symm.{u2, u2, u3, u4} R R M N (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) f)) v))
 but is expected to have type
-  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7] (b : Basis.{u4, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (f : LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M N _inst_2 _inst_7 _inst_3 _inst_8) (v : ι -> N), Eq.{max (succ u4) (succ u3)} (Matrix.{u4, u4, u3} ι ι R) (Basis.toMatrix.{u4, u4, u3, u1} ι ι R N _inst_1 _inst_7 _inst_8 (Basis.map.{u4, u3, u2, u1} ι R M N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 _inst_7 _inst_8 b f) v) (Basis.toMatrix.{u4, u4, u3, u2} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u4, succ u1, succ u2} ι N M (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => M) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) R N M (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} N _inst_7) (Module.toDistribMulAction.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} N _inst_7) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) f)) v))
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7] (b : Basis.{u4, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (f : LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M N _inst_2 _inst_7 _inst_3 _inst_8) (v : ι -> N), Eq.{max (succ u4) (succ u3)} (Matrix.{u4, u4, u3} ι ι R) (Basis.toMatrix.{u4, u4, u3, u1} ι ι R N _inst_1 _inst_7 _inst_8 (Basis.map.{u4, u3, u2, u1} ι R M N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 _inst_7 _inst_8 b f) v) (Basis.toMatrix.{u4, u4, u3, u2} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u4, succ u1, succ u2} ι N M (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : N) => M) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) R N M (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (DistribSMul.toSMulZeroClass.{u3, u1} R N (AddMonoid.toAddZeroClass.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (DistribMulAction.toDistribSMul.{u3, u1} R N (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} N _inst_7) (Module.toDistribMulAction.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) R N M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} N _inst_7) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, u2, max u2 u1} R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, u2, max u2 u1} R R N M (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, u2} R R N M (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearEquiv.symm.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) f)) v))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map Basis.toMatrix_mapₓ'. -/
 @[simp]
 theorem Basis.toMatrix_map (b : Basis ι R M) (f : M ≃ₗ[R] N) (v : ι → N) :

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

@@ -189,7 +189,7 @@ theorem sum_toMatrix_smul_self [Fintype ι] : (∑ i : ι, e.toMatrix v i j •
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u4}} [_inst_7 : Ring.{u4} S] [_inst_8 : Algebra.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7)] [_inst_9 : Fintype.{u1} ι] (b : Basis.{u1, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toAddCommGroup.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) (v : ι' -> S), Eq.{max (succ u2) (succ u4)} (ι' -> S) (Matrix.vecMul.{u4, u1, u2} ι ι' S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7))) _inst_9 (coeFn.{max (succ u1) (succ u3) (succ u4), max (succ u1) (succ u4)} (Basis.{u1, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toAddCommGroup.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) (fun (_x : Basis.{u1, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toAddCommGroup.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) => ι -> S) (FunLike.hasCoeToFun.{max (succ u1) (succ u3) (succ u4), succ u1, succ u4} (Basis.{u1, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toAddCommGroup.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) ι (fun (_x : ι) => S) (Basis.funLike.{u1, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toAddCommGroup.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8))) b) (Matrix.map.{u3, u4, u1, u2} ι ι' R S (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R S _inst_1 (AddCommGroup.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toAddCommGroup.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8) b v) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) (fun (_x : RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) => R -> S) (RingHom.hasCoeToFun.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) (algebraMap.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)))) v
 but is expected to have type
-  forall {ι : Type.{u2}} {ι' : Type.{u1}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u4}} [_inst_7 : Ring.{u4} S] [_inst_8 : Algebra.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7)] [_inst_9 : Fintype.{u2} ι] (b : Basis.{u2, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) (v : ι' -> S), Eq.{max (succ u1) (succ u4)} (ι' -> S) (Matrix.vecMul.{u4, u2, u1} ι ι' S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7))) _inst_9 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), succ u2, succ u4} (Basis.{u2, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => S) _x) (Basis.funLike.{u2, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) b) (Matrix.map.{u3, u4, u2, u1} ι ι' R S (Basis.toMatrix.{u2, u1, u3, u4} ι ι' R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8) b v) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7)))))) (algebraMap.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)))) v
+  forall {ι : Type.{u2}} {ι' : Type.{u1}} {R : Type.{u3}} [_inst_1 : CommSemiring.{u3} R] {S : Type.{u4}} [_inst_7 : Ring.{u4} S] [_inst_8 : Algebra.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7)] [_inst_9 : Fintype.{u2} ι] (b : Basis.{u2, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) (v : ι' -> S), Eq.{max (succ u1) (succ u4)} (ι' -> S) (Matrix.vecMul.{u4, u2, u1} ι ι' S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7))) _inst_9 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u4), succ u2, succ u4} (Basis.{u2, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => S) _x) (Basis.funLike.{u2, u3, u4} ι R S (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)) b) (Matrix.map.{u3, u4, u2, u1} ι ι' R S (Basis.toMatrix.{u2, u1, u3, u4} ι ι' R S _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} S (NonAssocRing.toNonUnitalNonAssocRing.{u4} S (Ring.toNonAssocRing.{u4} S _inst_7)))) (Algebra.toModule.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8) b v) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R S (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7))) R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7)) (RingHom.instRingHomClassRingHom.{u3, u4} R S (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} S (Ring.toSemiring.{u4} S _inst_7)))))) (algebraMap.{u3, u4} R S _inst_1 (Ring.toSemiring.{u4} S _inst_7) _inst_8)))) v
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMulₓ'. -/
 theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v :=
@@ -328,7 +328,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 lean 3 declaration is
   forall {ι : Type.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] [_inst_12 : Fintype.{u1} ι] (b : Basis.{u1, u2, max u1 u2} ι R (ι -> R) (CommSemiring.toSemiring.{u2} R _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (A : Matrix.{u1, u1, u2} ι ι R), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R) (Matrix.mul.{u2, u1, u1, u1} ι ι ι R _inst_12 (Distrib.toHasMul.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{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)))) (Basis.toMatrix.{u1, u1, u2, max u1 u2} ι ι R (ι -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) b (coeFn.{max (succ u1) (succ u2) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (Basis.{u1, u2, max u1 u2} ι R (ι -> R) (CommSemiring.toSemiring.{u2} R _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (j : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (fun (_x : Basis.{u1, u2, max u1 u2} ι R (ι -> R) (CommSemiring.toSemiring.{u2} R _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (j : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} 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(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))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : ι -> R) => Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (ι -> R) (AddMonoid.toZero.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (ι -> R) (AddMonoid.toAddZeroClass.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : ι -> R) => Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (ι -> R) (AddMonoid.toZero.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (ι -> R) (AddMonoid.toAddZeroClass.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b) (Matrix.transpose.{u1, u2, u2} ι ι R A j)) i))
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mulₓ'. -/
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
@@ -358,7 +358,7 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] [_inst_9 : Fintype.{u2} ι'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'] (b : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u1, succ u2} ι ι'), Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} ι' ι' R) (Basis.toMatrix.{u2, u2, u3, u4} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u1, u2, u3, u4} ι ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 b e) v) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgEquiv.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgEquiv.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) => (Matrix.{u1, u1, u3} ι ι R) -> (Matrix.{u2, u2, u3} ι' ι' R)) (AlgEquiv.hasCoeToFun.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) (Matrix.reindexAlgEquiv.{u1, u2, u3} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u1, u1, u3, u4} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u1, succ u2, succ u4} ι ι' M v (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e))))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι] [_inst_14 : DecidableEq.{succ u3} ι'] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u3} ι ι'), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι' ι' R) (Basis.toMatrix.{u3, u3, u2, u1} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u3, u2, u1} ι ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 b e) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (Matrix.{u4, u4, u2} ι ι R) (fun (_x : Matrix.{u4, u4, u2} ι ι R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u4, u4, u2} ι ι R) => Matrix.{u3, u3, u2} ι' ι' R) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (SMulZeroClass.toSMul.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (AddMonoid.toZero.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u4 u2, max u3 u2, max (max u4 u3) u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u4 u2, max u3 u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (Matrix.reindexAlgEquiv.{u4, u3, u2} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u4, u4, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u4, succ u3, succ u1} ι ι' M v (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e))))
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι] [_inst_14 : DecidableEq.{succ u3} ι'] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u3} ι ι'), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι' ι' R) (Basis.toMatrix.{u3, u3, u2, u1} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u3, u2, u1} ι ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 b e) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R 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(Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) 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(Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)))) (Module.toDistribMulAction.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Semiring.toNonAssocSemiring.{max u4 u2} (Matrix.{u4, u4, u2} ι ι R) (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b))))) (Algebra.toModule.{u2, max u4 u2} R (Matrix.{u4, u4, u2} ι ι R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} ι' ι' R) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b))))) (Algebra.toModule.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u4 u2, max u3 u2, max (max u4 u3) u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) (AlgEquivClass.toAlgHomClass.{max (max u4 u3) u2, u2, max u4 u2, max u3 u2} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))) R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u4 u2, max u3 u2} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u2, u3} ι' R (CommSemiring.toSemiring.{u2} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u4, u2} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))))))) (Matrix.reindexAlgEquiv.{u4, u3, u2} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u4, u4, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u4, succ u3, succ u1} ι ι' M v (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (Equiv.{succ u4, succ u3} ι ι') ι (fun (_x : ι) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e))))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex' Basis.toMatrix_reindex'ₓ'. -/
 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
@@ -417,7 +417,7 @@ def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂
 lean 3 declaration is
   forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (b : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u1, succ u2} ι ι'), Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} ι' ι' R) (Basis.toMatrix.{u2, u2, u3, u4} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u1, u2, u3, u4} ι ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 b e) v) (Matrix.submatrix.{u3, u2, u1, u2, u2} ι' ι ι' ι' R (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R M _inst_1 _inst_2 _inst_3 b v) (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} ι' ι) (fun (_x : Equiv.{succ u2, succ u1} ι' ι) => ι' -> ι) (Equiv.hasCoeToFun.{succ u2, succ u1} ι' ι) (Equiv.symm.{succ u1, succ u2} ι ι' e)) (id.{succ u2} ι'))
 but is expected to have type
-  forall {ι : Type.{u4}} {ι' : Type.{u1}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (b : Basis.{u4, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u1} ι ι'), Eq.{max (succ u1) (succ u3)} (Matrix.{u1, u1, u3} ι' ι' R) (Basis.toMatrix.{u1, u1, u3, u2} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u1, u3, u2} ι ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 b e) v) (Matrix.submatrix.{u3, u1, u4, u1, u1} ι' ι ι' ι' R (Basis.toMatrix.{u4, u1, u3, u2} ι ι' R M _inst_1 _inst_2 _inst_3 b v) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (Equiv.{succ u1, succ u4} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u4} ι' ι) (Equiv.symm.{succ u4, succ u1} ι ι' e)) (id.{succ u1} ι'))
+  forall {ι : Type.{u4}} {ι' : Type.{u1}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (b : Basis.{u4, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u1} ι ι'), Eq.{max (succ u1) (succ u3)} (Matrix.{u1, u1, u3} ι' ι' R) (Basis.toMatrix.{u1, u1, u3, u2} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u1, u3, u2} ι ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 b e) v) (Matrix.submatrix.{u3, u1, u4, u1, u1} ι' ι ι' ι' R (Basis.toMatrix.{u4, u1, u3, u2} ι ι' R M _inst_1 _inst_2 _inst_3 b v) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (Equiv.{succ u1, succ u4} ι' ι) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : ι') => ι) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u4} ι' ι) (Equiv.symm.{succ u4, succ u1} ι ι' e)) (id.{succ u1} ι'))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex Basis.toMatrix_reindexₓ'. -/
 @[simp]
 theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι') :

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

@@ -328,7 +328,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{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)))) (Basis.toMatrix.{u1, u1, u2, max u1 u2} ι ι R (ι -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) b (coeFn.{max (succ u1) (succ u2) (succ 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 but is expected to have type
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2663 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b) (Matrix.transpose.{u1, u2, u2} ι ι R A j)) i))
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mulₓ'. -/
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -148,7 +148,7 @@ theorem toMatrix_update [DecidableEq ι'] (x : M) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R₂ : Type.{u2}} {M₂ : Type.{u3}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u2, u3} R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_7 : DecidableEq.{succ u1} ι] (e : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (w : ι -> (Units.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R₂) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 e (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (fun (_x : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) => ι -> M₂) (FunLike.hasCoeToFun.{max (succ u1) (succ u2) (succ u3), succ u1, succ u3} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => M₂) (Basis.funLike.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6)) (Basis.unitsSMul.{u1, u2, u3} ι R₂ M₂ (CommRing.toRing.{u2} R₂ _inst_4) _inst_5 _inst_6 e w))) (Matrix.diagonal.{u2, u1} ι R₂ (fun (a : ι) (b : ι) => _inst_7 a b) (MulZeroClass.toHasZero.{u2} R₂ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R₂ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) (Function.comp.{succ u1, succ u2, succ u2} ι (Units.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))) R₂ ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))) R₂ (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))) R₂ (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))) R₂ (coeBase.{succ u2, succ u2} (Units.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))) R₂ (Units.hasCoe.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))))))) w))
 but is expected to have type
-  forall {ι : Type.{u3}} {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_7 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (w : ι -> (Units.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R₂) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M₂) _x) (Basis.funLike.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Basis.unitsSMul.{u3, u2, u1} ι R₂ M₂ (CommRing.toRing.{u2} R₂ _inst_4) _inst_5 _inst_6 e w))) (Matrix.diagonal.{u2, u3} ι R₂ (fun (a : ι) (b : ι) => _inst_7 a b) (CommMonoidWithZero.toZero.{u2} R₂ (CommSemiring.toCommMonoidWithZero.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))) (Function.comp.{succ u3, succ u2, succ u2} ι (Units.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))))) R₂ (Units.val.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))))) w))
+  forall {ι : Type.{u3}} {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_7 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (w : ι -> (Units.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)))))), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R₂) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M₂) _x) (Basis.funLike.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Basis.unitsSMul.{u3, u2, u1} ι R₂ M₂ (CommRing.toRing.{u2} R₂ _inst_4) _inst_5 _inst_6 e w))) (Matrix.diagonal.{u2, u3} ι R₂ (fun (a : ι) (b : ι) => _inst_7 a b) (CommMonoidWithZero.toZero.{u2} R₂ (CommSemiring.toCommMonoidWithZero.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))) (Function.comp.{succ u3, succ u2, succ u2} ι (Units.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))))) R₂ (Units.val.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))))) w))
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_units_smul Basis.toMatrix_unitsSMulₓ'. -/
 /-- The basis constructed by `units_smul` has vectors given by a diagonal matrix. -/
 @[simp]
@@ -165,7 +165,7 @@ theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι →
 lean 3 declaration is
   forall {ι : Type.{u1}} {R₂ : Type.{u2}} {M₂ : Type.{u3}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u2, u3} R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_7 : DecidableEq.{succ u1} ι] (e : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) {w : ι -> R₂} (hw : forall (i : ι), IsUnit.{u2} R₂ (Ring.toMonoid.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (w i)), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R₂) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 e (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (fun (_x : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) => ι -> M₂) (FunLike.hasCoeToFun.{max (succ u1) (succ u2) (succ u3), succ u1, succ u3} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => M₂) (Basis.funLike.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6)) (Basis.isUnitSMul.{u1, u2, u3} ι R₂ M₂ (CommRing.toRing.{u2} R₂ _inst_4) _inst_5 _inst_6 e (fun (i : ι) => w i) hw))) (Matrix.diagonal.{u2, u1} ι R₂ (fun (a : ι) (b : ι) => _inst_7 a b) (MulZeroClass.toHasZero.{u2} R₂ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R₂ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) w)
 but is expected to have type
-  forall {ι : Type.{u3}} {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_7 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) {w : ι -> R₂} (hw : forall (i : ι), IsUnit.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))) (w i)), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R₂) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M₂) _x) (Basis.funLike.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Basis.isUnitSMul.{u3, u2, u1} ι R₂ M₂ (CommRing.toRing.{u2} R₂ _inst_4) _inst_5 _inst_6 e (fun (i : ι) => w i) hw))) (Matrix.diagonal.{u2, u3} ι R₂ (fun (a : ι) (b : ι) => _inst_7 a b) (CommMonoidWithZero.toZero.{u2} R₂ (CommSemiring.toCommMonoidWithZero.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))) w)
+  forall {ι : Type.{u3}} {R₂ : Type.{u2}} {M₂ : Type.{u1}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u1} M₂] [_inst_6 : Module.{u2, u1} R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5)] [_inst_7 : DecidableEq.{succ u3} ι] (e : Basis.{u3, u2, u1} ι R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) {w : ι -> R₂} (hw : forall (i : ι), IsUnit.{u2} R₂ (MonoidWithZero.toMonoid.{u2} R₂ (Semiring.toMonoidWithZero.{u2} R₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)))) (w i)), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R₂) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6 e (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M₂) _x) (Basis.funLike.{u3, u2, u1} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_5) _inst_6) (Basis.isUnitSMul.{u3, u2, u1} ι R₂ M₂ (CommRing.toRing.{u2} R₂ _inst_4) _inst_5 _inst_6 e (fun (i : ι) => w i) hw))) (Matrix.diagonal.{u2, u3} ι R₂ (fun (a : ι) (b : ι) => _inst_7 a b) (CommMonoidWithZero.toZero.{u2} R₂ (CommSemiring.toCommMonoidWithZero.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))) w)
 Case conversion may be inaccurate. Consider using '#align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSMulₓ'. -/
 /-- The basis constructed by `is_unit_smul` has vectors given by a diagonal matrix. -/
 @[simp]
@@ -405,7 +405,7 @@ theorem Basis.toMatrix_mul_toMatrix_flip [DecidableEq ι] [Fintype ι'] :
 lean 3 declaration is
   forall {ι : Type.{u1}} {R₂ : Type.{u2}} {M₂ : Type.{u3}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u2, u3} R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : DecidableEq.{succ u1} ι] [_inst_10 : Fintype.{u1} ι] (b : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (b' : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6), Invertible.{max u1 u2} (Matrix.{u1, u1, u2} ι ι R₂) (Matrix.hasMul.{u2, u1} ι R₂ _inst_10 (Distrib.toHasMul.{u2} R₂ (Ring.toDistrib.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} R₂ (NonUnitalNonAssocRing.toAddCommGroup.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) (Matrix.hasOne.{u2, u1} ι R₂ (fun (a : ι) (b : ι) => _inst_9 a b) (MulZeroClass.toHasZero.{u2} R₂ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R₂ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) (AddMonoidWithOne.toOne.{u2} R₂ (AddGroupWithOne.toAddMonoidWithOne.{u2} R₂ (AddCommGroupWithOne.toAddGroupWithOne.{u2} R₂ (Ring.toAddCommGroupWithOne.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 b (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (fun (_x : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) => ι -> M₂) (FunLike.hasCoeToFun.{max (succ u1) (succ u2) (succ u3), succ u1, succ u3} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => M₂) (Basis.funLike.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6)) b'))
 but is expected to have type
-  forall {ι : Type.{u1}} {R₂ : Type.{u2}} {M₂ : Type.{u3}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u2, u3} R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : DecidableEq.{succ u1} ι] [_inst_10 : Fintype.{u1} ι] (b : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (b' : Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6), Invertible.{max u1 u2} (Matrix.{u1, u1, u2} ι ι R₂) (Matrix.instMulMatrix.{u2, u1} ι R₂ _inst_10 (NonUnitalNonAssocRing.toMul.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₂ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) (Matrix.one.{u2, u1} ι R₂ (fun (a : ι) (b : ι) => _inst_9 a b) (CommMonoidWithZero.toZero.{u2} R₂ (CommSemiring.toCommMonoidWithZero.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))) (NonAssocRing.toOne.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 b (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u1, succ u3} (Basis.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M₂) _x) (Basis.funLike.{u1, u2, u3} ι R₂ M₂ (Ring.toSemiring.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) b'))
+  forall {ι : Type.{u1}} {R₂ : Type.{u2}} {M₂ : Type.{u3}} [_inst_4 : CommRing.{u2} R₂] [_inst_5 : AddCommGroup.{u3} M₂] [_inst_6 : Module.{u2, u3} R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5)] [_inst_9 : DecidableEq.{succ u1} ι] [_inst_10 : Fintype.{u1} ι] (b : Basis.{u1, u2, u3} ι R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) (b' : Basis.{u1, u2, u3} ι R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6), Invertible.{max u1 u2} (Matrix.{u1, u1, u2} ι ι R₂) (Matrix.instMulMatrix.{u2, u1} ι R₂ _inst_10 (NonUnitalNonAssocRing.toMul.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R₂ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R₂ (NonAssocRing.toNonUnitalNonAssocRing.{u2} R₂ (Ring.toNonAssocRing.{u2} R₂ (CommRing.toRing.{u2} R₂ _inst_4)))))) (Matrix.one.{u2, u1} ι R₂ (fun (a : ι) (b : ι) => _inst_9 a b) (CommMonoidWithZero.toZero.{u2} R₂ (CommSemiring.toCommMonoidWithZero.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4))) (Semiring.toOne.{u2} R₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)))) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R₂ M₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6 b (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u1, succ u3} (Basis.{u1, u2, u3} ι R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M₂) _x) (Basis.funLike.{u1, u2, u3} ι R₂ M₂ (CommSemiring.toSemiring.{u2} R₂ (CommRing.toCommSemiring.{u2} R₂ _inst_4)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_5) _inst_6) b'))
 Case conversion may be inaccurate. Consider using '#align basis.invertible_to_matrix Basis.invertibleToMatrixₓ'. -/
 /-- A matrix whose columns form a basis `b'`, expressed w.r.t. a basis `b`, is invertible. -/
 def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂ M₂) :

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

@@ -328,7 +328,7 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{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)))) (Basis.toMatrix.{u1, u1, u2, max u1 u2} ι ι R (ι -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) b (coeFn.{max (succ u1) (succ u2) (succ 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_inst_1))))) (Finsupp.addCommMonoid.{u1, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Finsupp.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Basis.repr.{u1, u2, max u1 u2} ι R (ι -> R) (CommSemiring.toSemiring.{u2} R _inst_1) (Pi.addCommMonoid.{u1, u2} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Pi.Function.module.{u1, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) b) (Matrix.transpose.{u2, u1, u1} ι ι R A j)) i))
 but is expected to have type
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(NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))) (Basis.toMatrix.{u2, u2, u1, max u2 u1} ι ι R (ι -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (Basis.{u2, u1, max u1 u2} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => ι -> R) _x) (Basis.funLike.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.basisFun.{u1, u2} R ι (CommSemiring.toSemiring.{u1} R _inst_1) _inst_12))) A) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (ι -> R) (fun (_x : ι -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : ι -> R) => Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (ι -> R) (AddMonoid.toZero.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (ι -> R) (AddMonoid.toAddZeroClass.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b) (Matrix.transpose.{u1, u2, u2} ι ι R A j)) i))
+  forall {ι : Type.{u2}} {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] [_inst_12 : Fintype.{u2} ι] (b : Basis.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (A : Matrix.{u2, u2, u1} ι ι R), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} ι ι R) (Matrix.mul.{u1, u2, u2, u2} ι ι ι R _inst_12 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(fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (Basis.{u2, u1, max u1 u2} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => ι -> R) _x) (Basis.funLike.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.basisFun.{u1, u2} R ι (CommSemiring.toSemiring.{u1} R _inst_1) _inst_12))) A) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ 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(Semiring.toMonoidWithZero.{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} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u2, u1, max u2 u1} ι R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (ᾰ : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2669 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) b) (Matrix.transpose.{u1, u2, u2} ι ι R A j)) i))
 Case conversion may be inaccurate. Consider using '#align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mulₓ'. -/
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.basis
-! leanprover-community/mathlib commit 6c263e4bfc2e6714de30f22178b4d0ca4d149a76
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Matrix.ToLin
 /-!
 # Bases and matrices
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the map `basis.to_matrix` that sends a family of vectors to
 the matrix of their coordinates with respect to some basis.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -53,23 +53,43 @@ variable {R₂ M₂ : Type _} [CommRing R₂] [AddCommGroup M₂] [Module R₂ M
 
 open Function Matrix
 
+#print Basis.toMatrix /-
 /-- From a basis `e : ι → M` and a family of vectors `v : ι' → M`, make the matrix whose columns
 are the vectors `v i` written in the basis `e`. -/
 def Basis.toMatrix (e : Basis ι R M) (v : ι' → M) : Matrix ι ι' R := fun i j => e.repr (v j) i
 #align basis.to_matrix Basis.toMatrix
+-/
 
 variable (e : Basis ι R M) (v : ι' → M) (i : ι) (j : ι')
 
 namespace Basis
 
+/- warning: basis.to_matrix_apply -> Basis.toMatrix_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] (e : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (i : ι) (j : ι'), Eq.{succ u3} R (Basis.toMatrix.{u1, u2, u3, u4} ι ι' R M _inst_1 _inst_2 _inst_3 e v i j) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (fun (_x : Finsupp.{u1, u3} ι R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) => ι -> R) 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R _inst_1)))))) _inst_2 (Finsupp.addCommMonoid.{u1, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u1, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (fun (_x : LinearEquiv.{u3, u3, u4, max u1 u3} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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_inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (Basis.repr.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) (v j)) i)
+but is expected to have type
+  forall {ι : Type.{u3}} {ι' : Type.{u2}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] (e : Basis.{u3, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (i : ι) (j : ι'), Eq.{succ u4} R (Basis.toMatrix.{u3, u2, u4, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v i j) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (Finsupp.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), succ u1, max (succ u3) (succ u4)} (LinearEquiv.{u4, u4, u1, max u4 u3} R R (CommSemiring.toSemiring.{u4} R 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+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_apply Basis.toMatrix_applyₓ'. -/
 theorem toMatrix_apply : e.toMatrix v i j = e.repr (v j) i :=
   rfl
 #align basis.to_matrix_apply Basis.toMatrix_apply
 
+/- warning: basis.to_matrix_transpose_apply -> Basis.toMatrix_transpose_apply is a dubious translation:
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(CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u1, u3, u1, max u4 u3} (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u4 u3} (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u3, max u4 u3} R (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, u1, max u4 u3, max (max u4 u3) u1} R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u1, max u4 u3, max (max u4 u3) u1} R R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearEquiv.{u3, u3, u1, max u3 u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u1, max u4 u3} R R M (Finsupp.{u4, u3} ι R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u4, u3} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_3 (Finsupp.module.{u4, u3, u3} ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (Basis.repr.{u4, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 e) (v j)))
+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_applyₓ'. -/
 theorem toMatrix_transpose_apply : (e.toMatrix v)ᵀ j = e.repr (v j) :=
   funext fun _ => rfl
 #align basis.to_matrix_transpose_apply Basis.toMatrix_transpose_apply
 
+/- warning: basis.to_matrix_eq_to_matrix_constr -> Basis.toMatrix_eq_toMatrix_constr is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u1} ι] [_inst_8 : DecidableEq.{succ u1} ι] (v : ι -> M), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R M _inst_1 _inst_2 _inst_3 e v) (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ u3) (succ (max u1 u2))} (LinearEquiv.{u2, u2, u3, max u1 u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.toMatrix._proof_1.{u2} R _inst_1) (LinearMap.toMatrix._proof_2.{u2} R _inst_1) (LinearMap.{u2, u2, u3, 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+but is expected to have type
+  forall {ι : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) [_inst_7 : Fintype.{u3} ι] [_inst_8 : DecidableEq.{succ u3} ι] (v : ι -> M), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι ι R) (Basis.toMatrix.{u3, u3, u2, u1} ι ι R M _inst_1 _inst_2 _inst_3 e v) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R 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(RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} ι ι R) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u2, max u3 u2} R (Matrix.{u3, u3, u2} ι ι R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} ι ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u3 u2, max (max u3 u2) u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u3, u2} ι ι R) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u3, u2} ι ι R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) M M _inst_2 _inst_2 _inst_3 _inst_3) (SMulZeroClass.toSMul.{0, max u3 u1} Nat (ι -> M) (AddMonoid.toZero.{max u3 u1} (ι -> M) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)))) (DistribSMul.toSMulZeroClass.{0, max u3 u1} Nat (ι -> M) (AddMonoid.toAddZeroClass.{max u3 u1} (ι -> M) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)))) (DistribMulAction.toDistribSMul.{0, max u3 u1} Nat (ι -> M) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2))) (Module.toDistribMulAction.{0, max u3 u1} Nat (ι -> M) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, 0, max u3 u1, u1} (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{0} Nat (Semiring.toMonoidWithZero.{0} Nat Nat.semiring)) (AddCommMonoid.toAddMonoid.{max u3 u1} (ι -> M) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{0, max u3 u1} Nat (ι -> M) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2))) (Module.toDistribMulAction.{0, u1} Nat (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) Nat.semiring (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (SemilinearMapClass.distribMulActionHomClass.{0, max u3 u1, u1, max u3 u1} Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) Nat.semiring (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) Nat Nat.semiring (fun (i : ι) => _inst_2) (fun (i : ι) => AddCommMonoid.natModule.{u1} M _inst_2)) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, 0, u1, u1} R R Nat M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) Nat.semiring (AddCommMonoid.natModule.{u1} M _inst_2) (AddMonoid.nat_smulCommClass'.{u2, u1} R M (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))) (SemilinearEquivClass.instSemilinearMapClass.{0, 0, max u3 u1, u1, max u3 u1} Nat Nat (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{0, 0, max u3 u1, u1} Nat Nat Nat.semiring Nat.semiring (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHom.id.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) (RingHomInvPair.ids.{0} Nat Nat.semiring) (RingHomInvPair.ids.{0} Nat Nat.semiring) (ι -> M) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Pi.addCommMonoid.{u3, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) (fun (i : ι) => _inst_2)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Pi.module.{u3, u1, 0} ι (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.7822 : ι) => M) 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+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constrₓ'. -/
 theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M) :
     e.toMatrix v = LinearMap.toMatrix e e (e.constr ℕ v) :=
   by
@@ -77,14 +97,26 @@ theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M)
   rw [Basis.toMatrix_apply, LinearMap.toMatrix_apply, Basis.constr_basis]
 #align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constr
 
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+Case conversion may be inaccurate. Consider using '#align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transposeₓ'. -/
 -- TODO (maybe) Adjust the definition of `basis.to_matrix` to eliminate the transpose.
-theorem CoePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
+theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
     ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose :=
   by
   ext (M i j)
   rfl
-#align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.CoePiBasisFun.toMatrix_eq_transpose
-
+#align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transpose
+
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+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_self Basis.toMatrix_selfₓ'. -/
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   by
@@ -93,6 +125,12 @@ theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 :=
   simp [Basis.equivFun, Matrix.one_apply, Finsupp.single_apply, eq_comm]
 #align basis.to_matrix_self Basis.toMatrix_self
 
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+  forall {ι : Type.{u3}} {ι' : Type.{u4}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] (e : Basis.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (j : ι') [_inst_7 : DecidableEq.{succ u4} ι'] (x : M), Eq.{max (max (succ u3) (succ u4)) (succ u2)} (Matrix.{u3, u4, u2} ι ι' R) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e (Function.update.{succ u4, succ u1} ι' (fun (ᾰ : ι') => M) (fun (a : ι') (b : ι') => _inst_7 a b) v j x)) (Matrix.updateColumn.{u2, u3, u4} ι ι' R (fun (a : ι') (b : ι') => _inst_7 a b) (Basis.toMatrix.{u3, u4, u2, u1} ι ι' R M _inst_1 _inst_2 _inst_3 e v) j (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u1, max (succ u3) (succ u2)} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R 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(Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u2, u1, max u3 u2} (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} M _inst_2) (AddCommMonoid.toAddMonoid.{max u3 u2} (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (Module.toDistribMulAction.{u2, max u3 u2} R (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u3 u2, max (max u3 u2) u1} R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearEquiv.{u2, u2, u1, max u2 u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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(RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u3 u2} R R M (Finsupp.{u3, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (Finsupp.addCommMonoid.{u3, u2} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) _inst_3 (Finsupp.module.{u3, u2, u2} ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (Basis.repr.{u3, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 e) x)))
+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_update Basis.toMatrix_updateₓ'. -/
 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) :=
   by
@@ -103,29 +141,53 @@ theorem toMatrix_update [DecidableEq ι'] (x : M) :
   · rw [update_noteq h]
 #align basis.to_matrix_update Basis.toMatrix_update
 
+/- warning: basis.to_matrix_units_smul -> Basis.toMatrix_unitsSMul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_units_smul Basis.toMatrix_unitsSMulₓ'. -/
 /-- The basis constructed by `units_smul` has vectors given by a diagonal matrix. -/
 @[simp]
-theorem toMatrix_unitsSmul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι → R₂ˣ) :
+theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι → R₂ˣ) :
     e.toMatrix (e.units_smul w) = diagonal (coe ∘ w) :=
   by
   ext (i j)
   by_cases h : i = j
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def]
   · simp [h, to_matrix_apply, units_smul_apply, Units.smul_def, Ne.symm h]
-#align basis.to_matrix_units_smul Basis.toMatrix_unitsSmul
-
+#align basis.to_matrix_units_smul Basis.toMatrix_unitsSMul
+
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 /-- The basis constructed by `is_unit_smul` has vectors given by a diagonal matrix. -/
 @[simp]
-theorem toMatrix_isUnitSmul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι → R₂}
-    (hw : ∀ i, IsUnit (w i)) : e.toMatrix (e.isUnitSmul hw) = diagonal w :=
-  e.toMatrix_unitsSmul _
-#align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSmul
-
+theorem toMatrix_isUnitSMul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι → R₂}
+    (hw : ∀ i, IsUnit (w i)) : e.toMatrix (e.isUnitSMul hw) = diagonal w :=
+  e.toMatrix_unitsSMul _
+#align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSMul
+
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 @[simp]
 theorem sum_toMatrix_smul_self [Fintype ι] : (∑ i : ι, e.toMatrix v i j • e i) = v j := by
   simp_rw [e.to_matrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 
+/- warning: basis.to_matrix_map_vec_mul -> Basis.toMatrix_map_vecMul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMulₓ'. -/
 theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v :=
   by
@@ -134,12 +196,19 @@ theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b
     sum_to_matrix_smul_self]
 #align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMul
 
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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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u4 u3) u2} (Matrix.{u4, u3, u2} ι ι' R) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max (max u4 u3) u2} R (Matrix.{u4, u3, u2} ι ι' R) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) 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_inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max (max u4 u3) u2, u1, max (max (max u4 u3) u2) u1} R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (LinearEquiv.{u2, u2, max (max u2 u3) u4, 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, 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(CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max (max u4 u3) u2, u1} R R (Matrix.{u4, u3, u2} ι ι' R) (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (Matrix.addCommMonoid.{u2, u4, u3} ι ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.module.{u2, u4, u3, u2} ι ι' R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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+Case conversion may be inaccurate. Consider using '#align basis.to_lin_to_matrix Basis.toLin_toMatrixₓ'. -/
 @[simp]
 theorem toLin_toMatrix [Fintype ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
     Matrix.toLin v e (e.toMatrix v) = id :=
   v.ext fun i => by rw [to_lin_self, id_apply, e.sum_to_matrix_smul_self]
 #align basis.to_lin_to_matrix Basis.toLin_toMatrix
 
+#print Basis.toMatrixEquiv /-
 /-- From a basis `e : ι → M`, build a linear equivalence between families of vectors `v : ι → M`,
 and matrices, making the matrix whose columns are the vectors `v i` written in the basis `e`. -/
 def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix ι ι R
@@ -166,6 +235,7 @@ def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix
     simp only [e.to_matrix_apply, ← e.equiv_fun_apply, ← e.equiv_fun_symm_apply,
       LinearEquiv.apply_symm_apply]
 #align basis.to_matrix_equiv Basis.toMatrixEquiv
+-/
 
 end Basis
 
@@ -183,6 +253,12 @@ section Fintype
 
 variable [Fintype ι'] [Fintype κ] [Fintype κ']
 
+/- warning: basis_to_matrix_mul_linear_map_to_matrix -> basis_toMatrix_mul_linearMap_toMatrix is a dubious translation:
+lean 3 declaration is
+  forall {ι' : Type.{u1}} {κ : Type.{u2}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u1, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u2, u4, u6} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u1} ι'] [_inst_10 : Fintype.{u2} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : 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_inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u2, u1, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1)) (LinearMap.toMatrix.{u4, u2, u1, u5, u6} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_12 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c) f)
+but is expected to have type
+  forall {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : 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_inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u6 u5) u4, max (max (max (max u6 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u6 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u6, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u6, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (LinearMap.toMatrix.{u4, u5, u6, u1, u2} R _inst_1 κ ι' _inst_9 _inst_10 (fun (a : ι') (b : ι') => _inst_12 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b' c) f)
+Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul_linear_map_to_matrix basis_toMatrix_mul_linearMap_toMatrixₓ'. -/
 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
@@ -194,6 +270,12 @@ theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
 
 variable [Fintype ι]
 
+/- warning: linear_map_to_matrix_mul_basis_to_matrix -> linearMap_toMatrix_mul_basis_toMatrix is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b : Basis.{u1, u4, u5} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c' : Basis.{u3, u4, u6} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u5, u6} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u2} ι'] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'], Eq.{succ (max u3 u1 u4)} (Matrix.{u3, u1, u4} κ' ι R) (Matrix.mul.{u4, u3, u2, u1} κ' ι' ι R _inst_9 (Distrib.toHasMul.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (coeFn.{max (succ (max u5 u6)) (succ (max u3 u2 u4)), max (succ (max u5 u6)) (succ (max u3 u2 u4))} (LinearEquiv.{u4, u4, max u5 u6, max u3 u2 u4} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) 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_inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u4} κ' ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u5, u6} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u1} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.module.{u4, u4, u4, u5, u6} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u4, u3, u1, u4} κ' ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.toMatrix._proof_1.{u4} R _inst_1) (LinearMap.toMatrix._proof_2.{u4} R _inst_1)) (LinearMap.toMatrix.{u4, u3, u1, u5, u6} R _inst_1 κ' ι _inst_12 _inst_11 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c') f)
+but is expected to have type
+  forall {ι : Type.{u6}} {ι' : Type.{u5}} {κ' : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7] (b : Basis.{u6, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u5, u3, u2} ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (c' : Basis.{u4, u3, u1} κ' R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u5} ι'] [_inst_11 : Fintype.{u4} κ'] [_inst_12 : Fintype.{u6} ι] [_inst_13 : 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(CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, 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(LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u4) u3} (Matrix.{u4, u6, u3} κ' ι R) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, max u2 u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u3, max (max u6 u4) u3} R (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, max u2 u1, max (max u6 u4) u3, max (max (max (max u6 u4) u3) u2) u1} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearEquiv.{u3, u3, max u1 u2, max (max u3 u6) u4} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, max u2 u1, max (max u6 u4) u3} R R (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u6, u3} κ' ι R) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (LinearMap.addCommMonoid.{u3, u3, u2, u1} R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Matrix.addCommMonoid.{u3, u4, u6} κ' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u2, u1} R R R M N (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (smulCommClass_self.{u3, u1} R N (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u3, u4, u6, u3} κ' ι R R (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (LinearMap.toMatrix.{u3, u4, u6, u2, u1} R _inst_1 κ' ι _inst_12 _inst_11 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c') f)
+Case conversion may be inaccurate. Consider using '#align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrixₓ'. -/
 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c' f :=
@@ -201,11 +283,23 @@ theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι']
     (by rw [to_lin_to_matrix, to_lin_mul b b' c', to_lin_to_matrix, b'.to_lin_to_matrix, comp_id])
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
 
+/- warning: basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix -> basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ : Type.{u3}} {κ' : Type.{u4}} {R : Type.{u5}} {M : Type.{u6}} [_inst_1 : CommSemiring.{u5} R] [_inst_2 : AddCommMonoid.{u6} M] [_inst_3 : Module.{u5, u6} R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2] {N : Type.{u7}} [_inst_7 : AddCommMonoid.{u7} N] [_inst_8 : Module.{u5, u7} R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7] (b : Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u2, u5, u6} ι' R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (c : Basis.{u3, u5, u7} κ R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u3} κ] [_inst_11 : Fintype.{u4} κ'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'], Eq.{succ (max u3 u1 u5)} (Matrix.{u3, u1, u5} κ ι R) (Matrix.mul.{u5, u3, u2, u1} κ ι' ι R _inst_9 (Distrib.toHasMul.{u5} R (NonUnitalNonAssocSemiring.toDistrib.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.mul.{u5, u3, u4, u2} κ κ' ι' R _inst_11 (Distrib.toHasMul.{u5} R (NonUnitalNonAssocSemiring.toDistrib.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Basis.toMatrix.{u3, u4, u5, u7} κ κ' R N _inst_1 _inst_7 _inst_8 c (coeFn.{max (succ u4) (succ u5) (succ u7), max (succ u4) (succ u7)} (Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) (fun (_x : Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) => κ' -> N) (FunLike.hasCoeToFun.{max (succ u4) (succ u5) (succ u7), succ u4, succ u7} (Basis.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8) κ' (fun (_x : κ') => N) (Basis.funLike.{u4, u5, u7} κ' R N (CommSemiring.toSemiring.{u5} R _inst_1) _inst_7 _inst_8)) c')) (coeFn.{max (succ (max u6 u7)) (succ (max u4 u2 u5)), max (succ (max u6 u7)) (succ (max u4 u2 u5))} (LinearEquiv.{u5, u5, max u6 u7, max u4 u2 u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R 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(RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (LinearMap.toMatrix._proof_1.{u5} R _inst_1) (LinearMap.toMatrix._proof_2.{u5} R _inst_1) (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u4, u2, u5} κ' ι' R) (LinearMap.addCommMonoid.{u5, u5, u6, u7} R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.addCommMonoid.{u5, u4, u2} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u4, u2, u5} κ' ι' R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) => (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u4, u2, u5} κ' ι' R)) (LinearEquiv.hasCoeToFun.{u5, u5, max u6 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_inst_2 _inst_7 _inst_3 _inst_8 b' c') f)) (Basis.toMatrix.{u2, u1, u5, u6} ι' ι R M _inst_1 _inst_2 _inst_3 b' (coeFn.{max (succ u1) (succ u5) (succ u6), max (succ u1) (succ u6)} (Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) (fun (_x : Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) => ι -> M) (FunLike.hasCoeToFun.{max (succ u1) (succ u5) (succ u6), succ u1, succ u6} (Basis.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3) ι (fun (_x : ι) => M) (Basis.funLike.{u1, u5, u6} ι R M (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_3)) b))) (coeFn.{max (succ (max u6 u7)) (succ (max u3 u1 u5)), max (succ (max u6 u7)) (succ (max u3 u1 u5))} (LinearEquiv.{u5, u5, max u6 u7, max u3 u1 u5} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R 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_inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u3, u1, u5} κ ι R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) => (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) -> (Matrix.{u3, u1, u5} κ ι R)) (LinearEquiv.hasCoeToFun.{u5, u5, max u6 u7, max u3 u1 u5} R R (LinearMap.{u5, u5, u6, u7} R R (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u1, u5} κ ι R) (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) (LinearMap.addCommMonoid.{u5, u5, u6, u7} R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Matrix.addCommMonoid.{u5, u3, u1} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))))) (LinearMap.module.{u5, u5, u5, u6, u7} R R R M N (CommSemiring.toSemiring.{u5} R _inst_1) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (CommSemiring.toSemiring.{u5} R _inst_1) _inst_8 (LinearMap.toMatrix._proof_3.{u5, u7} R _inst_1 N _inst_7 _inst_8)) (Matrix.module.{u5, u3, u1, u5} κ ι R R (CommSemiring.toSemiring.{u5} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u5} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1)))) (Semiring.toModule.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (RingHom.id.{u5} R (Semiring.toNonAssocSemiring.{u5} R (CommSemiring.toSemiring.{u5} R _inst_1))) (LinearMap.toMatrix._proof_1.{u5} R _inst_1) (LinearMap.toMatrix._proof_2.{u5} R _inst_1)) (LinearMap.toMatrix.{u5, u3, u1, u6, u7} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b c) f)
+but is expected to have type
+  forall {ι : Type.{u7}} {ι' : Type.{u6}} {κ : Type.{u5}} {κ' : Type.{u3}} {R : Type.{u4}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u4, u1} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u2}} [_inst_7 : AddCommMonoid.{u2} N] [_inst_8 : Module.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] (b : Basis.{u7, u4, u1} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b' : Basis.{u6, u4, u1} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (c : Basis.{u5, u4, u2} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (c' : Basis.{u3, u4, u2} κ' R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (f : LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) [_inst_9 : Fintype.{u6} ι'] [_inst_10 : Fintype.{u5} κ] [_inst_11 : Fintype.{u3} κ'] [_inst_12 : Fintype.{u7} ι] [_inst_13 : DecidableEq.{succ u7} ι] [_inst_14 : DecidableEq.{succ u6} ι'], Eq.{max (max (succ u7) (succ u5)) (succ u4)} (Matrix.{u5, u7, u4} κ ι R) (Matrix.mul.{u4, u5, u6, u7} κ ι' ι R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.mul.{u4, u5, u3, u6} κ κ' ι' R _inst_11 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} 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(Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u6 u3) u4} (Matrix.{u3, u6, u4} κ' ι' R) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u6 u3) u4} R (Matrix.{u3, u6, u4} κ' ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u6 u3) u4, max (max (max (max u6 u3) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u6) u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u3, u6, u4} κ' ι' R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u3, u6} κ' ι' R 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u3, u6, u4} κ' ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R 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(CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u2} (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u7 u5) u4} (Matrix.{u5, u7, u4} κ ι R) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u1 u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u7 u5) u4} R (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u1 u2, max (max u7 u5) u4, max (max (max (max u7 u5) u4) u1) u2} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (LinearEquiv.{u4, u4, max u2 u1, max (max u4 u7) 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_inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, max u1 u2, max (max u7 u5) u4} R R (LinearMap.{u4, u4, u1, u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u5, u7, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u2} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u7} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u2} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u2} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u2} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u2} N (AddCommMonoid.toAddMonoid.{u2} N _inst_7)) (Module.toMulActionWithZero.{u4, u2} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u5, u7, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrixₓ'. -/
 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c f := by
   rw [basis_toMatrix_mul_linearMap_toMatrix, linearMap_toMatrix_mul_basis_toMatrix]
 #align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
 
+/- warning: basis_to_matrix_mul -> basis_toMatrix_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {κ : Type.{u3}} {R : Type.{u4}} {M : Type.{u5}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u5} M] [_inst_3 : Module.{u4, u5} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u6}} [_inst_7 : AddCommMonoid.{u6} N] [_inst_8 : Module.{u4, u6} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u3} κ] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u3} κ] (b₁ : Basis.{u1, u4, u5} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u2, u4, u5} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u3, u4, u6} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u3, u4} ι' κ R), Eq.{succ (max u1 u3 u4)} (Matrix.{u1, u3, u4} ι κ R) (Matrix.mul.{u4, u1, u2, u3} ι ι' κ R _inst_9 (Distrib.toHasMul.{u4} R (NonUnitalNonAssocSemiring.toDistrib.{u4} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u6, u5} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u3, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.module.{u4, u4, u4, u6, u5} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (Matrix.toLin._proof_3.{u4, u5} R _inst_1 M _inst_2 _inst_3)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1)) (Matrix.toLin.{u4, u2, u3, u6, u5} R _inst_1 ι' κ _inst_10 _inst_9 (fun (a : κ) (b : κ) => _inst_13 a b) N M _inst_7 _inst_2 _inst_8 _inst_3 b₃ b₂) A))
+but is expected to have type
+  forall {ι : Type.{u5}} {ι' : Type.{u2}} {κ : Type.{u6}} {R : Type.{u4}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u2} ι'] [_inst_10 : Fintype.{u6} κ] [_inst_12 : Fintype.{u5} ι] [_inst_13 : DecidableEq.{succ u6} κ] (b₁ : Basis.{u5, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u2, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u6, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u6, u4} ι' κ R), Eq.{max (max (succ u5) (succ u6)) (succ u4)} (Matrix.{u5, u6, u4} ι κ R) (Matrix.mul.{u4, u5, u2, u6} ι ι' κ R _inst_9 (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} 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u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (SMulZeroClass.toSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toZero.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (AddMonoid.toAddZeroClass.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u5 u6) u4) u3) u1, u4, max u3 u1, max (max u5 u6) u4} (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u6) u4} (Matrix.{u5, u6, u4} ι κ R) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (Module.toDistribMulAction.{u4, max (max u5 u6) u4} R (Matrix.{u5, u6, u4} ι κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u3 u1, max (max u5 u6) u4, max (max (max (max u5 u6) u4) u3) u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u5, u6} ι κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u4, u5, u6, u4} ι κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max u3 u1, max (max u5 u6) u4, max (max (max (max u5 u6) u4) u3) u1} R R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.{u5, u6, u4} ι κ R) (LinearEquiv.{u4, u4, max u3 u1, max (max u4 u6) u5} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R 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_inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u2 u6) u4) u3) u1, u4, max (max u2 u6) u4, max u3 u1} (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} 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(AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u2 u6) u4} (Matrix.{u2, u6, u4} ι' κ R) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u2 u6) u4} R (Matrix.{u2, u6, u4} ι' κ R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3))))) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u1, u3} R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} ι' κ R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u1, u3} R R R N M (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3 (smulCommClass_self.{u4, u3} R M (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u3} R M (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_2)) (Module.toMulActionWithZero.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, max (max u2 u6) u4, max u3 u1, max (max (max (max u2 u6) u4) u3) u1} R R (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u3 u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} ι' κ R) (LinearMap.{u4, u4, u1, u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) N M _inst_7 _inst_2 _inst_8 _inst_3) (Matrix.addCommMonoid.{u4, u2, u6} ι' κ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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+Case conversion may be inaccurate. Consider using '#align basis_to_matrix_mul basis_toMatrix_mulₓ'. -/
 theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
     (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) :=
   by
@@ -213,6 +307,12 @@ theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis
   rwa [LinearMap.toMatrix_toLin] at this
 #align basis_to_matrix_mul basis_toMatrix_mul
 
+/- warning: mul_basis_to_matrix -> mul_basis_toMatrix is a dubious translation:
+lean 3 declaration is
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(CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (Matrix.toLin._proof_3.{u4, u6} R _inst_1 N _inst_7 _inst_8)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (Matrix.toLin._proof_1.{u4} R _inst_1) (Matrix.toLin._proof_2.{u4} R _inst_1)) (Matrix.toLin.{u4, u3, u1, u5, u6} R _inst_1 κ ι _inst_12 _inst_10 (fun (a : ι) (b : ι) => _inst_13 a b) M N _inst_2 _inst_7 _inst_3 _inst_8 b₁ b₃) A))
+but is expected to have type
+  forall {ι : Type.{u6}} {ι' : Type.{u5}} {κ : Type.{u2}} {R : Type.{u4}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u4, u3} R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7] [_inst_9 : Fintype.{u5} ι'] [_inst_10 : Fintype.{u2} κ] [_inst_12 : Fintype.{u6} ι] [_inst_13 : DecidableEq.{succ u6} ι] [_inst_14 : DecidableEq.{succ u5} ι'] (b₁ : Basis.{u6, u4, u3} ι R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₂ : Basis.{u5, u4, u3} ι' R M (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_3) (b₃ : Basis.{u2, u4, u1} κ R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8) (A : Matrix.{u2, u6, u4} κ ι R), Eq.{max (max (succ u5) (succ u2)) (succ u4)} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.mul.{u4, u2, u6, u5} κ ι ι' R _inst_12 (NonUnitalNonAssocSemiring.toMul.{u4} R 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(Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (SMulZeroClass.toSMul.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (AddMonoid.toZero.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (AddMonoid.toAddZeroClass.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u5 u2) u4) u3) u1, u4, max u3 u1, max (max u5 u2) u4} (LinearEquiv.{u4, u4, max u1 u3, max (max u4 u5) u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max (max u5 u2) u4} (Matrix.{u2, u5, u4} κ ι' R) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (Module.toDistribMulAction.{u4, max (max u5 u2) u4} R (Matrix.{u2, u5, u4} κ ι' R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u4, max u3 u1, max (max u5 u2) u4, max (max (max (max u5 u2) u4) u3) u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (LinearEquiv.{u4, u4, max u1 u3, max (max u4 u5) u2} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.{u2, u5, u4} κ ι' R) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.addCommMonoid.{u4, u2, u5} κ ι' R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))) (Matrix.module.{u4, u2, u5, u4} κ ι' R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N 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(LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddMonoid.toAddZeroClass.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max (max u6 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(CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u6 u2) u4} (Matrix.{u2, u6, u4} κ ι R) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Module.toDistribMulAction.{u4, max (max u6 u2) u4} R (Matrix.{u2, u6, u4} κ ι R) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Module.toDistribMulAction.{u4, max u3 u1} R (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (CommSemiring.toSemiring.{u4} R _inst_1) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (SemilinearMapClass.distribMulActionHomClass.{u4, max (max u6 u2) u4, max u3 u1, max (max (max (max u6 u2) u4) u3) u1} R (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (LinearEquiv.{u4, u4, max (max u4 u6) u2, max u1 u3} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (Matrix.{u2, u6, u4} κ ι R) (LinearMap.{u4, u4, u3, u1} R R (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) M N _inst_2 _inst_7 _inst_3 _inst_8) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u4, u4, u3, u1} R R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_8 (smulCommClass_self.{u4, u1} R N (CommSemiring.toCommMonoid.{u4} R _inst_1) (MulActionWithZero.toMulAction.{u4, u1} R N (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N _inst_7)) (Module.toMulActionWithZero.{u4, u1} R N (CommSemiring.toSemiring.{u4} R _inst_1) _inst_7 _inst_8))))) (CommSemiring.toSemiring.{u4} R _inst_1) (Matrix.addCommMonoid.{u4, u2, u6} κ ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (LinearMap.addCommMonoid.{u4, u4, u3, u1} R R M N (CommSemiring.toSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1)))) (Matrix.module.{u4, u2, u6, u4} κ ι R R (CommSemiring.toSemiring.{u4} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R 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+Case conversion may be inaccurate. Consider using '#align mul_basis_to_matrix mul_basis_toMatrixₓ'. -/
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
     A ⬝ b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) :=
@@ -221,6 +321,12 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
   rwa [LinearMap.toMatrix_toLin] at this
 #align mul_basis_to_matrix mul_basis_toMatrix
 
+/- warning: basis_to_matrix_basis_fun_mul -> basis_toMatrix_basisFun_mul is a dubious translation:
+lean 3 declaration is
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(CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (ι -> R) (AddMonoid.toZero.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (ι -> R) (AddMonoid.toAddZeroClass.{max u2 u1} (ι -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (ι -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{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} (ι -> R) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (ι -> R) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, max u2 u1} R (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, max u2 u1, max u1 u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (ι -> R) (Finsupp.{u2, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Pi.module.{u2, u1, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) R (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (i : ι) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Finsupp.module.{u2, u1, u1} ι R 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)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u1} ι (fun (a._@.Mathlib.LinearAlgebra.Matrix.Basis._hyg.2673 : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.addCommMonoid.{u2, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mulₓ'. -/
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
   classical
@@ -230,6 +336,12 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
       Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 
+/- warning: linear_map.to_matrix_id_eq_basis_to_matrix -> LinearMap.toMatrix_id_eq_basis_toMatrix is a dubious translation:
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(RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Matrix.addCommMonoid.{u2, u3, u4} ι' ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max (max u4 u3) u2, max (max (max u4 u3) u2) u1} R R (LinearMap.{u2, 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))) M M _inst_2 _inst_2 _inst_3 _inst_3) (Matrix.{u3, u4, u2} ι' ι R) (LinearEquiv.{u2, u2, u1, max (max u2 u4) u3} 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))) (RingHom.id.{u2} R 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(LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R 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u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_2 _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R _inst_1) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_2)) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3)))) (Matrix.module.{u2, u3, u4, u2} ι' ι R 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)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} 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+Case conversion may be inaccurate. Consider using '#align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrixₓ'. -/
 /-- A generalization of `linear_map.to_matrix_id`. -/
 @[simp]
 theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
@@ -239,6 +351,12 @@ theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
   rw [← @basis_toMatrix_mul_linearMap_toMatrix _ _ ι, to_matrix_id, Matrix.mul_one]
 #align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrix
 
+/- warning: basis.to_matrix_reindex' -> Basis.toMatrix_reindex' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {ι' : Type.{u2}} {R : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u4} M] [_inst_3 : Module.{u3, u4} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] [_inst_9 : Fintype.{u2} ι'] [_inst_12 : Fintype.{u1} ι] [_inst_13 : DecidableEq.{succ u1} ι] [_inst_14 : DecidableEq.{succ u2} ι'] (b : Basis.{u1, u3, u4} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u1, succ u2} ι ι'), Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} ι' ι' R) (Basis.toMatrix.{u2, u2, u3, u4} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u1, u2, u3, u4} ι ι' R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3 b e) v) (coeFn.{max (succ (max u1 u3)) (succ (max u2 u3)), max (succ (max u1 u3)) (succ (max u2 u3))} (AlgEquiv.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) (fun (_x : AlgEquiv.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) => (Matrix.{u1, u1, u3} ι ι R) -> (Matrix.{u2, u2, u3} ι' ι' R)) (AlgEquiv.hasCoeToFun.{u3, max u1 u3, max u2 u3} R (Matrix.{u1, u1, u3} ι ι R) (Matrix.{u2, u2, u3} ι' ι' R) _inst_1 (Matrix.semiring.{u3, u1} ι R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b)) (Matrix.semiring.{u3, u2} ι' R (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b)) (Matrix.algebra.{u3, u1, u3} ι R R _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) (Matrix.algebra.{u3, u2, u3} ι' R R _inst_9 (fun (a : ι') (b : ι') => _inst_14 a b) _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))) (Matrix.reindexAlgEquiv.{u1, u2, u3} ι ι' R _inst_1 _inst_9 _inst_12 (fun (a : ι) (b : ι) => _inst_13 a b) (fun (a : ι') (b : ι') => _inst_14 a b) e) (Basis.toMatrix.{u1, u1, u3, u4} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u1, succ u2, succ u4} ι ι' M v (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} ι ι') (fun (_x : Equiv.{succ u1, succ u2} ι ι') => ι -> ι') (Equiv.hasCoeToFun.{succ u1, succ u2} ι ι') e))))
+but is expected to have type
+  forall {ι : Type.{u4}} {ι' : Type.{u3}} {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] [_inst_9 : Fintype.{u3} ι'] [_inst_12 : Fintype.{u4} ι] [_inst_13 : DecidableEq.{succ u4} ι] [_inst_14 : DecidableEq.{succ u3} ι'] (b : Basis.{u4, u2, u1} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (v : ι' -> M) (e : Equiv.{succ u4, succ u3} ι ι'), Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} ι' ι' R) (Basis.toMatrix.{u3, u3, u2, u1} ι' ι' R M _inst_1 _inst_2 _inst_3 (Basis.reindex.{u4, u3, u2, u1} ι ι' R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 b e) v) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u2), max (succ u4) (succ u2), max (succ u3) (succ u2)} (AlgEquiv.{u2, max u2 u4, max u2 u3} R (Matrix.{u4, u4, u2} ι ι R) (Matrix.{u3, u3, u2} ι' ι' R) _inst_1 (Matrix.semiring.{u2, u4} ι R (CommSemiring.toSemiring.{u2} R 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(x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : ι) => ι') _x) (Equiv.instFunLikeEquiv.{succ u4, succ u3} ι ι') e))))
+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_reindex' Basis.toMatrix_reindex'ₓ'. -/
 /-- See also `basis.to_matrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
     (e : ι ≃ ι') : (b.reindex e).toMatrix v = Matrix.reindexAlgEquiv _ e (b.toMatrix (v ∘ e)) :=
@@ -251,6 +369,12 @@ theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι
 
 end Fintype
 
+/- warning: basis.to_matrix_mul_to_matrix -> Basis.toMatrix_mul_toMatrix is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_mul_to_matrix Basis.toMatrix_mul_toMatrixₓ'. -/
 /-- A generalization of `basis.to_matrix_self`, in the opposite direction. -/
 @[simp]
 theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' → M) :
@@ -263,17 +387,35 @@ theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' 
   simp only [Matrix.mul_apply, Basis.toMatrix_apply, Basis.sum_repr_mul_repr]
 #align basis.to_matrix_mul_to_matrix Basis.toMatrix_mul_toMatrix
 
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 /-- `b.to_matrix b'` and `b'.to_matrix b` are inverses. -/
 theorem Basis.toMatrix_mul_toMatrix_flip [DecidableEq ι] [Fintype ι'] :
     b.toMatrix b' ⬝ b'.toMatrix b = 1 := by rw [Basis.toMatrix_mul_toMatrix, Basis.toMatrix_self]
 #align basis.to_matrix_mul_to_matrix_flip Basis.toMatrix_mul_toMatrix_flip
 
+/- warning: basis.invertible_to_matrix -> Basis.invertibleToMatrix is a dubious translation:
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 /-- A matrix whose columns form a basis `b'`, expressed w.r.t. a basis `b`, is invertible. -/
 def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂ M₂) :
     Invertible (b.toMatrix b') :=
   ⟨b'.toMatrix b, Basis.toMatrix_mul_toMatrix_flip _ _, Basis.toMatrix_mul_toMatrix_flip _ _⟩
 #align basis.invertible_to_matrix Basis.invertibleToMatrix
 
+/- warning: basis.to_matrix_reindex -> Basis.toMatrix_reindex is a dubious translation:
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 @[simp]
 theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι') :
     (b.reindex e).toMatrix v = (b.toMatrix v).submatrix e.symm id :=
@@ -283,6 +425,12 @@ theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι
     Finsupp.mapDomain_equiv_apply]
 #align basis.to_matrix_reindex Basis.toMatrix_reindex
 
+/- warning: basis.to_matrix_map -> Basis.toMatrix_map is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : AddCommMonoid.{u3} M] [_inst_3 : Module.{u2, u3} R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2] {N : Type.{u4}} [_inst_7 : AddCommMonoid.{u4} N] [_inst_8 : Module.{u2, u4} R N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7] (b : Basis.{u1, u2, u3} ι R M (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3) (f : LinearEquiv.{u2, u2, u3, u4} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) M N _inst_2 _inst_7 _inst_3 _inst_8) (v : ι -> N), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} ι ι R) (Basis.toMatrix.{u1, u1, u2, u4} ι ι R N _inst_1 _inst_7 _inst_8 (Basis.map.{u1, u2, u3, u4} ι R M N (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_3 _inst_7 _inst_8 b f) v) (Basis.toMatrix.{u1, u1, u2, u3} ι ι R M _inst_1 _inst_2 _inst_3 b (Function.comp.{succ u1, succ u4, succ u3} ι N M (coeFn.{max (succ u4) (succ u3), max (succ u4) (succ u3)} (LinearEquiv.{u2, u2, u4, u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) (fun (_x : LinearEquiv.{u2, u2, u4, u3} 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))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) N M _inst_7 _inst_2 _inst_8 _inst_3) => N -> M) (LinearEquiv.hasCoeToFun.{u2, u2, u4, u3} R R N M (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_7 _inst_2 _inst_8 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (LinearEquiv.symm.{u2, u2, u3, u4} R R M N (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 _inst_7 _inst_3 _inst_8 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) f)) v))
+but is expected to have type
+  forall {ι : Type.{u4}} {R : Type.{u3}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2] {N : Type.{u1}} [_inst_7 : AddCommMonoid.{u1} N] [_inst_8 : Module.{u3, u1} R N (CommSemiring.toSemiring.{u3} R _inst_1) _inst_7] (b : Basis.{u4, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3) (f : LinearEquiv.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) M N _inst_2 _inst_7 _inst_3 _inst_8) (v : ι -> N), Eq.{max (succ u4) (succ u3)} (Matrix.{u4, u4, u3} ι ι R) 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(SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u3, u2} R M (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u1, u2} (LinearEquiv.{u3, u3, u1, u2} R R (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R 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(CommSemiring.toSemiring.{u3} R _inst_1))) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) f)) v))
+Case conversion may be inaccurate. Consider using '#align basis.to_matrix_map Basis.toMatrix_mapₓ'. -/
 @[simp]
 theorem Basis.toMatrix_map (b : Basis ι R M) (f : M ≃ₗ[R] N) (v : ι → N) :
     (b.map f).toMatrix v = b.toMatrix (f.symm ∘ v) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

@@ -4,11 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.basis
-! leanprover-community/mathlib commit 2f4cdce0c2f2f3b8cd58f05d556d03b468e1eb2e
+! leanprover-community/mathlib commit 6c263e4bfc2e6714de30f22178b4d0ca4d149a76
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
 import Mathbin.LinearAlgebra.Matrix.Reindex
 import Mathbin.LinearAlgebra.Matrix.ToLin
 
@@ -272,7 +271,7 @@ theorem Basis.toMatrix_mul_toMatrix_flip [DecidableEq ι] [Fintype ι'] :
 /-- A matrix whose columns form a basis `b'`, expressed w.r.t. a basis `b`, is invertible. -/
 def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂ M₂) :
     Invertible (b.toMatrix b') :=
-  Matrix.invertibleOfLeftInverse _ _ (Basis.toMatrix_mul_toMatrix_flip _ _)
+  ⟨b'.toMatrix b, Basis.toMatrix_mul_toMatrix_flip _ _, Basis.toMatrix_mul_toMatrix_flip _ _⟩
 #align basis.invertible_to_matrix Basis.invertibleToMatrix
 
 @[simp]

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

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

@@ -280,7 +280,7 @@ def Basis.invertibleToMatrix [DecidableEq ι] [Fintype ι] (b b' : Basis ι R₂
 theorem Basis.toMatrix_reindex (b : Basis ι R M) (v : ι' → M) (e : ι ≃ ι') :
     (b.reindex e).toMatrix v = (b.toMatrix v).submatrix e.symm _root_.id := by
   ext
-  simp only [Basis.toMatrix_apply, Basis.repr_reindex, Matrix.submatrix_apply, id.def,
+  simp only [Basis.toMatrix_apply, Basis.repr_reindex, Matrix.submatrix_apply, _root_.id,
     Finsupp.mapDomain_equiv_apply]
 #align basis.to_matrix_reindex Basis.toMatrix_reindex
 

Also drop a no longer needed [DecidableEq _] argument in 1 lemma. It was needed to generate a computable Fintype (Set.range _) instance but a Finite instance doesn't need it.

@@ -131,9 +131,9 @@ theorem toMatrix_map_vecMul {S : Type*} [Ring S] [Algebra R S] [Fintype ι] (b :
 #align basis.to_matrix_map_vec_mul Basis.toMatrix_map_vecMul
 
 @[simp]
-theorem toLin_toMatrix [Fintype ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
+theorem toLin_toMatrix [Finite ι] [Fintype ι'] [DecidableEq ι'] (v : Basis ι' R M) :
     Matrix.toLin v e (e.toMatrix v) = LinearMap.id :=
-  v.ext fun i => by rw [toLin_self, id_apply, e.sum_toMatrix_smul_self]
+  v.ext fun i => by cases nonempty_fintype ι; rw [toLin_self, id_apply, e.sum_toMatrix_smul_self]
 #align basis.to_lin_to_matrix Basis.toLin_toMatrix
 
 /-- From a basis `e : ι → M`, build a linear equivalence between families of vectors `v : ι → M`,
@@ -185,39 +185,51 @@ open LinearMap
 
 section Fintype
 
-variable [Fintype ι'] [Fintype κ] [Fintype κ']
+/-- A generalization of `LinearMap.toMatrix_id`. -/
+@[simp]
+theorem LinearMap.toMatrix_id_eq_basis_toMatrix [Fintype ι] [DecidableEq ι] [Finite ι'] :
+    LinearMap.toMatrix b b' id = b'.toMatrix b := by
+  ext i
+  apply LinearMap.toMatrix_apply
+#align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrix
+
+variable [Fintype ι']
 
 @[simp]
-theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
+theorem basis_toMatrix_mul_linearMap_toMatrix [Finite κ] [Fintype κ'] [DecidableEq ι'] :
     c.toMatrix c' * LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
   (Matrix.toLin b' c).injective <| by
     haveI := Classical.decEq κ'
     rw [toLin_toMatrix, toLin_mul b' c' c, toLin_toMatrix, c.toLin_toMatrix, LinearMap.id_comp]
 #align basis_to_matrix_mul_linear_map_to_matrix basis_toMatrix_mul_linearMap_toMatrix
 
-variable [Fintype ι]
+theorem basis_toMatrix_mul [Fintype κ] [Finite ι] [DecidableEq κ]
+    (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N) (A : Matrix ι' κ R) :
+    b₁.toMatrix b₂ * A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) := by
+  have := basis_toMatrix_mul_linearMap_toMatrix b₃ b₁ b₂ (Matrix.toLin b₃ b₂ A)
+  rwa [LinearMap.toMatrix_toLin] at this
+#align basis_to_matrix_mul basis_toMatrix_mul
+
+variable [Finite κ] [Fintype ι]
 
 @[simp]
-theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
+theorem linearMap_toMatrix_mul_basis_toMatrix [Finite κ'] [DecidableEq ι] [DecidableEq ι'] :
     LinearMap.toMatrix b' c' f * b'.toMatrix b = LinearMap.toMatrix b c' f :=
   (Matrix.toLin b c').injective <| by
     rw [toLin_toMatrix, toLin_mul b b' c', toLin_toMatrix, b'.toLin_toMatrix, LinearMap.comp_id]
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
 
-theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
+theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
+    [Fintype κ'] [DecidableEq ι] [DecidableEq ι'] :
     c.toMatrix c' * LinearMap.toMatrix b' c' f * b'.toMatrix b = LinearMap.toMatrix b c f := by
+  cases nonempty_fintype κ
   rw [basis_toMatrix_mul_linearMap_toMatrix, linearMap_toMatrix_mul_basis_toMatrix]
 #align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
 
-theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
-    (A : Matrix ι' κ R) : b₁.toMatrix b₂ * A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) := by
-  have := basis_toMatrix_mul_linearMap_toMatrix b₃ b₁ b₂ (Matrix.toLin b₃ b₂ A)
-  rwa [LinearMap.toMatrix_toLin] at this
-#align basis_to_matrix_mul basis_toMatrix_mul
-
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
     A * b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) := by
+  cases nonempty_fintype κ
   have := linearMap_toMatrix_mul_basis_toMatrix b₂ b₁ b₃ (Matrix.toLin b₁ b₃ A)
   rwa [LinearMap.toMatrix_toLin] at this
 #align mul_basis_to_matrix mul_basis_toMatrix
@@ -225,20 +237,12 @@ theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
     b.toMatrix (Pi.basisFun R ι) * A = of fun i j => b.repr (Aᵀ j) i := by
   classical
-    simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
-    ext i j
-    rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
-      Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
+  simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
+  ext i j
+  rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
+    Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
 
-/-- A generalization of `LinearMap.toMatrix_id`. -/
-@[simp]
-theorem LinearMap.toMatrix_id_eq_basis_toMatrix [DecidableEq ι] :
-    LinearMap.toMatrix b b' id = b'.toMatrix b := by
-  haveI := Classical.decEq ι'
-  rw [← @basis_toMatrix_mul_linearMap_toMatrix _ _ ι, toMatrix_id, Matrix.mul_one]
-#align linear_map.to_matrix_id_eq_basis_to_matrix LinearMap.toMatrix_id_eq_basis_toMatrix
-
 /-- See also `Basis.toMatrix_reindex` which gives the `simp` normal form of this result. -/
 theorem Basis.toMatrix_reindex' [DecidableEq ι] [DecidableEq ι'] (b : Basis ι R M) (v : ι' → M)
     (e : ι ≃ ι') : (b.reindex e).toMatrix v = Matrix.reindexAlgEquiv _ e (b.toMatrix (v ∘ e)) := by

.. in equivOfPiLEquivPi, coePiBasisFun.toMatrix_eq_transpose, vecMul_surjective_iff_exists_left_inverse, and mulVec_surjective_iff_exists_right_inverse

@@ -72,7 +72,7 @@ theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M)
 #align basis.to_matrix_eq_to_matrix_constr Basis.toMatrix_eq_toMatrix_constr
 
 -- TODO (maybe) Adjust the definition of `Basis.toMatrix` to eliminate the transpose.
-theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
+theorem coePiBasisFun.toMatrix_eq_transpose [Finite ι] :
     ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by
   ext M i j
   rfl

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)

@@ -43,9 +43,7 @@ open Matrix
 section BasisToMatrix
 
 variable {ι ι' κ κ' : Type*}
-
 variable {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
-
 variable {R₂ M₂ : Type*} [CommRing R₂] [AddCommGroup M₂] [Module R₂ M₂]
 
 open Function Matrix
@@ -180,9 +178,7 @@ end Basis
 section MulLinearMapToMatrix
 
 variable {N : Type*} [AddCommMonoid N] [Module R N]
-
 variable (b : Basis ι R M) (b' : Basis ι' R M) (c : Basis κ R N) (c' : Basis κ' R N)
-
 variable (f : M →ₗ[R] N)
 
 open LinearMap

Prove that each class of the classgroup of a number field contains an integral ideal of small norm.

@@ -165,6 +165,16 @@ def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix
       LinearEquiv.apply_symm_apply]
 #align basis.to_matrix_equiv Basis.toMatrixEquiv
 
+variable (R₂) in
+theorem restrictScalars_toMatrix [Fintype ι] [DecidableEq ι] {S : Type*} [CommRing S] [Nontrivial S]
+    [Algebra R₂ S] [Module S M₂] [IsScalarTower R₂ S M₂] [NoZeroSMulDivisors R₂ S]
+    (b : Basis ι S M₂) (v : ι → span R₂ (Set.range b)) :
+    (algebraMap R₂ S).mapMatrix ((b.restrictScalars R₂).toMatrix v) =
+      b.toMatrix (fun i ↦ (v i : M₂)) := by
+  ext
+  rw [RingHom.mapMatrix_apply, Matrix.map_apply, Basis.toMatrix_apply,
+    Basis.restrictScalars_repr_apply, Basis.toMatrix_apply]
+
 end Basis
 
 section MulLinearMapToMatrix

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Notation.20for.20mul_vec.20and.20vec_mul

Co-authored-by: Martin Dvorak <mdvorak@ista.ac.at>

@@ -126,7 +126,7 @@ theorem toMatrix_smul {R₁ S : Type*} [CommRing R₁] [Ring S] [Algebra R₁ S]
   rfl
 
 theorem toMatrix_map_vecMul {S : Type*} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
-    (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v := by
+    (v : ι' → S) : b ᵥ* ((b.toMatrix v).map <| algebraMap R S) = v := by
   ext i
   simp_rw [vecMul, dotProduct, Matrix.map_apply, ← Algebra.commutes, ← Algebra.smul_def,
     sum_toMatrix_smul_self]

This PR defines the absolute ideal norm of a fractional ideal I : FractionalIdeal R⁰ K where K is a fraction field of R as a zero-preserving group homomorphism with values in ℚ and proves that it generalises the norm on (integral) ideals (and some other classical result).

Also in this PR:

• Add the directory Mathlib/RingTheory/FractionalIdeal and move the file Mathlib/RingTheory/FractionalIdeal.lean to Mathlib/RingTheory/FractionalIdeal/Basic.lean. The new results are in Mathlib/RingTheory/FractionalIdeal/Norm.lean
• Define the numerator and denominator of a fractional ideal. These are used to define the norm. Also define a linear equiv between a fractional ideal and its numerator.
• Several technical lemmas.

@@ -118,6 +118,13 @@ theorem sum_toMatrix_smul_self [Fintype ι] : ∑ i : ι, e.toMatrix v i j • e
   simp_rw [e.toMatrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 
+theorem toMatrix_smul {R₁ S : Type*} [CommRing R₁] [Ring S] [Algebra R₁ S] [Fintype ι]
+    [DecidableEq ι] (x : S) (b : Basis ι R₁ S) (w : ι → S) :
+    (b.toMatrix (x • w)) = (Algebra.leftMulMatrix b x) * (b.toMatrix w) := by
+  ext
+  rw [Basis.toMatrix_apply, Pi.smul_apply, smul_eq_mul, ← Algebra.leftMulMatrix_mulVec_repr]
+  rfl
+
 theorem toMatrix_map_vecMul {S : Type*} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v := by
   ext i

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

@@ -177,10 +177,9 @@ variable [Fintype ι'] [Fintype κ] [Fintype κ']
 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
     c.toMatrix c' * LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
-  (Matrix.toLin b' c).injective
-    (by
-      haveI := Classical.decEq κ'
-      rw [toLin_toMatrix, toLin_mul b' c' c, toLin_toMatrix, c.toLin_toMatrix, id_comp])
+  (Matrix.toLin b' c).injective <| by
+    haveI := Classical.decEq κ'
+    rw [toLin_toMatrix, toLin_mul b' c' c, toLin_toMatrix, c.toLin_toMatrix, LinearMap.id_comp]
 #align basis_to_matrix_mul_linear_map_to_matrix basis_toMatrix_mul_linearMap_toMatrix
 
 variable [Fintype ι]
@@ -188,8 +187,8 @@ variable [Fintype ι]
 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
     LinearMap.toMatrix b' c' f * b'.toMatrix b = LinearMap.toMatrix b c' f :=
-  (Matrix.toLin b c').injective
-    (by rw [toLin_toMatrix, toLin_mul b b' c', toLin_toMatrix, b'.toLin_toMatrix, comp_id])
+  (Matrix.toLin b c').injective <| by
+    rw [toLin_toMatrix, toLin_mul b b' c', toLin_toMatrix, b'.toLin_toMatrix, LinearMap.comp_id]
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
 
 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :

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).

@@ -176,7 +176,7 @@ variable [Fintype ι'] [Fintype κ] [Fintype κ']
 
 @[simp]
 theorem basis_toMatrix_mul_linearMap_toMatrix [DecidableEq ι'] :
-    c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
+    c.toMatrix c' * LinearMap.toMatrix b' c' f = LinearMap.toMatrix b' c f :=
   (Matrix.toLin b' c).injective
     (by
       haveI := Classical.decEq κ'
@@ -187,31 +187,31 @@ variable [Fintype ι]
 
 @[simp]
 theorem linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
-    LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c' f :=
+    LinearMap.toMatrix b' c' f * b'.toMatrix b = LinearMap.toMatrix b c' f :=
   (Matrix.toLin b c').injective
     (by rw [toLin_toMatrix, toLin_mul b b' c', toLin_toMatrix, b'.toLin_toMatrix, comp_id])
 #align linear_map_to_matrix_mul_basis_to_matrix linearMap_toMatrix_mul_basis_toMatrix
 
 theorem basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] :
-    c.toMatrix c' ⬝ LinearMap.toMatrix b' c' f ⬝ b'.toMatrix b = LinearMap.toMatrix b c f := by
+    c.toMatrix c' * LinearMap.toMatrix b' c' f * b'.toMatrix b = LinearMap.toMatrix b c f := by
   rw [basis_toMatrix_mul_linearMap_toMatrix, linearMap_toMatrix_mul_basis_toMatrix]
 #align basis_to_matrix_mul_linear_map_to_matrix_mul_basis_to_matrix basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix
 
 theorem basis_toMatrix_mul [DecidableEq κ] (b₁ : Basis ι R M) (b₂ : Basis ι' R M) (b₃ : Basis κ R N)
-    (A : Matrix ι' κ R) : b₁.toMatrix b₂ ⬝ A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) := by
+    (A : Matrix ι' κ R) : b₁.toMatrix b₂ * A = LinearMap.toMatrix b₃ b₁ (toLin b₃ b₂ A) := by
   have := basis_toMatrix_mul_linearMap_toMatrix b₃ b₁ b₂ (Matrix.toLin b₃ b₂ A)
   rwa [LinearMap.toMatrix_toLin] at this
 #align basis_to_matrix_mul basis_toMatrix_mul
 
 theorem mul_basis_toMatrix [DecidableEq ι] [DecidableEq ι'] (b₁ : Basis ι R M) (b₂ : Basis ι' R M)
     (b₃ : Basis κ R N) (A : Matrix κ ι R) :
-    A ⬝ b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) := by
+    A * b₁.toMatrix b₂ = LinearMap.toMatrix b₂ b₃ (toLin b₁ b₃ A) := by
   have := linearMap_toMatrix_mul_basis_toMatrix b₂ b₁ b₃ (Matrix.toLin b₁ b₃ A)
   rwa [LinearMap.toMatrix_toLin] at this
 #align mul_basis_to_matrix mul_basis_toMatrix
 
 theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι ι R) :
-    b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
+    b.toMatrix (Pi.basisFun R ι) * A = of fun i j => b.repr (Aᵀ j) i := by
   classical
     simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
     ext i j
@@ -241,7 +241,7 @@ end Fintype
 /-- A generalization of `Basis.toMatrix_self`, in the opposite direction. -/
 @[simp]
 theorem Basis.toMatrix_mul_toMatrix {ι'' : Type*} [Fintype ι'] (b'' : ι'' → M) :
-    b.toMatrix b' ⬝ b'.toMatrix b'' = b.toMatrix b'' := by
+    b.toMatrix b' * b'.toMatrix b'' = b.toMatrix b'' := by
   haveI := Classical.decEq ι
   haveI := Classical.decEq ι'
   haveI := Classical.decEq ι''
@@ -251,7 +251,7 @@ theorem Basis.toMatrix_mul_toMatrix {ι'' : Type*} [Fintype ι'] (b'' : ι'' →
 
 /-- `b.toMatrix b'` and `b'.toMatrix b` are inverses. -/
 theorem Basis.toMatrix_mul_toMatrix_flip [DecidableEq ι] [Fintype ι'] :
-    b.toMatrix b' ⬝ b'.toMatrix b = 1 := by rw [Basis.toMatrix_mul_toMatrix, Basis.toMatrix_self]
+    b.toMatrix b' * b'.toMatrix b = 1 := by rw [Basis.toMatrix_mul_toMatrix, Basis.toMatrix_self]
 #align basis.to_matrix_mul_to_matrix_flip Basis.toMatrix_mul_toMatrix_flip
 
 /-- A matrix whose columns form a basis `b'`, expressed w.r.t. a basis `b`, is invertible. -/

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

This has nice performance benefits.

@@ -42,11 +42,11 @@ open Matrix
 
 section BasisToMatrix
 
-variable {ι ι' κ κ' : Type _}
+variable {ι ι' κ κ' : Type*}
 
-variable {R M : Type _} [CommSemiring R] [AddCommMonoid M] [Module R M]
+variable {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
 
-variable {R₂ M₂ : Type _} [CommRing R₂] [AddCommGroup M₂] [Module R₂ M₂]
+variable {R₂ M₂ : Type*} [CommRing R₂] [AddCommGroup M₂] [Module R₂ M₂]
 
 open Function Matrix
 
@@ -118,7 +118,7 @@ theorem sum_toMatrix_smul_self [Fintype ι] : ∑ i : ι, e.toMatrix v i j • e
   simp_rw [e.toMatrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 
-theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
+theorem toMatrix_map_vecMul {S : Type*} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v := by
   ext i
   simp_rw [vecMul, dotProduct, Matrix.map_apply, ← Algebra.commutes, ← Algebra.smul_def,
@@ -162,7 +162,7 @@ end Basis
 
 section MulLinearMapToMatrix
 
-variable {N : Type _} [AddCommMonoid N] [Module R N]
+variable {N : Type*} [AddCommMonoid N] [Module R N]
 
 variable (b : Basis ι R M) (b' : Basis ι' R M) (c : Basis κ R N) (c' : Basis κ' R N)
 
@@ -240,7 +240,7 @@ end Fintype
 
 /-- A generalization of `Basis.toMatrix_self`, in the opposite direction. -/
 @[simp]
-theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' → M) :
+theorem Basis.toMatrix_mul_toMatrix {ι'' : Type*} [Fintype ι'] (b'' : ι'' → M) :
     b.toMatrix b' ⬝ b'.toMatrix b'' = b.toMatrix b'' := by
   haveI := Classical.decEq ι
   haveI := Classical.decEq ι'

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.basis
-! leanprover-community/mathlib commit 6c263e4bfc2e6714de30f22178b4d0ca4d149a76
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Matrix.Reindex
 import Mathlib.LinearAlgebra.Matrix.ToLin
 
+#align_import linear_algebra.matrix.basis from "leanprover-community/mathlib"@"6c263e4bfc2e6714de30f22178b4d0ca4d149a76"
+
 /-!
 # Bases and matrices
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -117,7 +117,7 @@ theorem toMatrix_isUnitSMul [DecidableEq ι] (e : Basis ι R₂ M₂) {w : ι 
 #align basis.to_matrix_is_unit_smul Basis.toMatrix_isUnitSMul
 
 @[simp]
-theorem sum_toMatrix_smul_self [Fintype ι] : (∑ i : ι, e.toMatrix v i j • e i) = v j := by
+theorem sum_toMatrix_smul_self [Fintype ι] : ∑ i : ι, e.toMatrix v i j • e i = v j := by
   simp_rw [e.toMatrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 

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>

@@ -79,20 +79,20 @@ theorem toMatrix_eq_toMatrix_constr [Fintype ι] [DecidableEq ι] (v : ι → M)
 -- TODO (maybe) Adjust the definition of `Basis.toMatrix` to eliminate the transpose.
 theorem coePiBasisFun.toMatrix_eq_transpose [Fintype ι] :
     ((Pi.basisFun R ι).toMatrix : Matrix ι ι R → Matrix ι ι R) = Matrix.transpose := by
-  ext (M i j)
+  ext M i j
   rfl
 #align basis.coe_pi_basis_fun.to_matrix_eq_transpose Basis.coePiBasisFun.toMatrix_eq_transpose
 
 @[simp]
 theorem toMatrix_self [DecidableEq ι] : e.toMatrix e = 1 := by
   unfold Basis.toMatrix
-  ext (i j)
+  ext i j
   simp [Basis.equivFun, Matrix.one_apply, Finsupp.single_apply, eq_comm]
 #align basis.to_matrix_self Basis.toMatrix_self
 
 theorem toMatrix_update [DecidableEq ι'] (x : M) :
     e.toMatrix (Function.update v j x) = Matrix.updateColumn (e.toMatrix v) j (e.repr x) := by
-  ext (i' k)
+  ext i' k
   rw [Basis.toMatrix, Matrix.updateColumn_apply, e.toMatrix_apply]
   split_ifs with h
   · rw [h, update_same j x v]
@@ -103,7 +103,7 @@ theorem toMatrix_update [DecidableEq ι'] (x : M) :
 @[simp]
 theorem toMatrix_unitsSMul [DecidableEq ι] (e : Basis ι R₂ M₂) (w : ι → R₂ˣ) :
     e.toMatrix (e.unitsSMul w) = diagonal ((↑) ∘ w) := by
-  ext (i j)
+  ext i j
   by_cases h : i = j
   · simp [h, toMatrix_apply, unitsSMul_apply, Units.smul_def]
   · simp [h, toMatrix_apply, unitsSMul_apply, Units.smul_def, Ne.symm h]
@@ -139,13 +139,13 @@ and matrices, making the matrix whose columns are the vectors `v i` written in t
 def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix ι ι R where
   toFun := e.toMatrix
   map_add' v w := by
-    ext (i j)
+    ext i j
     change _ = _ + _
     rw [e.toMatrix_apply, Pi.add_apply, LinearEquiv.map_add]
     rfl
   map_smul' := by
     intro c v
-    ext (i j)
+    ext i j
     dsimp only []
     rw [e.toMatrix_apply, Pi.smul_apply, LinearEquiv.map_smul]
     rfl
@@ -156,7 +156,7 @@ def toMatrixEquiv [Fintype ι] (e : Basis ι R M) : (ι → M) ≃ₗ[R] Matrix
     exact e.sum_toMatrix_smul_self v j
   right_inv := by
     intro m
-    ext (k l)
+    ext k l
     simp only [e.toMatrix_apply, ← e.equivFun_apply, ← e.equivFun_symm_apply,
       LinearEquiv.apply_symm_apply]
 #align basis.to_matrix_equiv Basis.toMatrixEquiv
@@ -217,7 +217,7 @@ theorem basis_toMatrix_basisFun_mul (b : Basis ι R (ι → R)) (A : Matrix ι 
     b.toMatrix (Pi.basisFun R ι) ⬝ A = of fun i j => b.repr (Aᵀ j) i := by
   classical
     simp only [basis_toMatrix_mul _ _ (Pi.basisFun R ι), Matrix.toLin_eq_toLin']
-    ext (i j)
+    ext i j
     rw [LinearMap.toMatrix_apply, Matrix.toLin'_apply, Pi.basisFun_apply,
       Matrix.mulVec_stdBasis_apply, Matrix.of_apply]
 #align basis_to_matrix_basis_fun_mul basis_toMatrix_basisFun_mul
@@ -248,7 +248,7 @@ theorem Basis.toMatrix_mul_toMatrix {ι'' : Type _} [Fintype ι'] (b'' : ι'' 
   haveI := Classical.decEq ι
   haveI := Classical.decEq ι'
   haveI := Classical.decEq ι''
-  ext (i j)
+  ext i j
   simp only [Matrix.mul_apply, Basis.toMatrix_apply, Basis.sum_repr_mul_repr]
 #align basis.to_matrix_mul_to_matrix Basis.toMatrix_mul_toMatrix
 

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -121,7 +121,6 @@ theorem sum_toMatrix_smul_self [Fintype ι] : (∑ i : ι, e.toMatrix v i j •
   simp_rw [e.toMatrix_apply, e.sum_repr]
 #align basis.sum_to_matrix_smul_self Basis.sum_toMatrix_smul_self
 
-set_option synthInstance.etaExperiment true in
 theorem toMatrix_map_vecMul {S : Type _} [Ring S] [Algebra R S] [Fintype ι] (b : Basis ι R S)
     (v : ι' → S) : ((b.toMatrix v).map <| algebraMap R S).vecMul b = v := by
   ext i

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Johan Commelin <johan@commelin.net>