linear_algebra.basis.bilinear ⟷ Mathlib.LinearAlgebra.Basis.Bilinear

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Mathbin.LinearAlgebra.Basis
-import Mathbin.LinearAlgebra.BilinearMap
+import LinearAlgebra.Basis
+import LinearAlgebra.BilinearMap
 
 #align_import linear_algebra.basis.bilinear from "leanprover-community/mathlib"@"832f7b9162039c28b9361289c8681f155cae758f"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module linear_algebra.basis.bilinear
-! leanprover-community/mathlib commit 832f7b9162039c28b9361289c8681f155cae758f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Basis
 import Mathbin.LinearAlgebra.BilinearMap
 
+#align_import linear_algebra.basis.bilinear from "leanprover-community/mathlib"@"832f7b9162039c28b9361289c8681f155cae758f"
+
 /-!
 # Lemmas about bilinear maps with a basis over each argument
 

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

@@ -45,12 +45,15 @@ variable {ρ₁₂ : R →+* R₂} {σ₁₂ : S →+* S₂}
 
 variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ R Mₗ) (b₂' : Basis ι₂ R Nₗ)
 
+#print LinearMap.ext_basis /-
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
     B = B' :=
   b₁.ext fun i => b₂.ext fun j => h i j
 #align linear_map.ext_basis LinearMap.ext_basis
+-/
 
+#print LinearMap.sum_repr_mul_repr_mulₛₗ /-
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for semi-bilinear maps, see `sum_repr_mul_repr_mul` for the bilinear version. -/
@@ -62,7 +65,9 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
   simp_rw [Finsupp.total_apply, Finsupp.sum, map_sum₂, map_sum, LinearMap.map_smulₛₗ₂,
     LinearMap.map_smulₛₗ]
 #align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗ
+-/
 
+#print LinearMap.sum_repr_mul_repr_mul /-
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for bilinear maps, see `sum_repr_mul_repr_mulₛₗ` for the semi-bilinear version. -/
@@ -74,6 +79,7 @@ theorem sum_repr_mul_repr_mul {B : Mₗ →ₗ[R] Nₗ →ₗ[R] Pₗ} (x y) :
   simp_rw [Finsupp.total_apply, Finsupp.sum, map_sum₂, map_sum, LinearMap.map_smul₂,
     LinearMap.map_smul]
 #align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mul
+-/
 
 end AddCommMonoid
 

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

@@ -45,18 +45,12 @@ variable {ρ₁₂ : R →+* R₂} {σ₁₂ : S →+* S₂}
 
 variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ R Mₗ) (b₂' : Basis ι₂ R Nₗ)
 
-/- warning: linear_map.ext_basis -> LinearMap.ext_basis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
     B = B' :=
   b₁.ext fun i => b₂.ext fun j => h i j
 #align linear_map.ext_basis LinearMap.ext_basis
 
-/- warning: linear_map.sum_repr_mul_repr_mulₛₗ -> LinearMap.sum_repr_mul_repr_mulₛₗ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for semi-bilinear maps, see `sum_repr_mul_repr_mul` for the bilinear version. -/
@@ -69,9 +63,6 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
     LinearMap.map_smulₛₗ]
 #align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗ
 
-/- warning: linear_map.sum_repr_mul_repr_mul -> LinearMap.sum_repr_mul_repr_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for bilinear maps, see `sum_repr_mul_repr_mulₛₗ` for the semi-bilinear version. -/

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

@@ -46,10 +46,7 @@ variable {ρ₁₂ : R →+* R₂} {σ₁₂ : S →+* S₂}
 variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ R Mₗ) (b₂' : Basis ι₂ R Nₗ)
 
 /- warning: linear_map.ext_basis -> LinearMap.ext_basis is a dubious translation:
-lean 3 declaration is
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u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) B B')
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
@@ -58,10 +55,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 #align linear_map.ext_basis LinearMap.ext_basis
 
 /- warning: linear_map.sum_repr_mul_repr_mulₛₗ -> LinearMap.sum_repr_mul_repr_mulₛₗ is a dubious translation:
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(RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) 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 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
@@ -76,10 +70,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 #align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗ
 
 /- warning: linear_map.sum_repr_mul_repr_mul -> LinearMap.sum_repr_mul_repr_mul is a dubious translation:
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(Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) 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B x) y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

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

@@ -49,7 +49,7 @@ variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 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(CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₂) => N) _x) (Basis.funLike.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) b₂ j))) -> (Eq.{max (max (succ u7) (succ u5)) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) B B')
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u3, u4, u7, max u8 u9} R R₂ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) ρ₁₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u9} P (Finsupp.sum.{u1, u3, u9} ι₁ R P (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R 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 but is expected to have type
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_inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R 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_inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddMonoid.toZero.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddMonoid.toAddZeroClass.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S 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(RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) 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(_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => S₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))))) σ₁₂ yj) (FunLike.coe.{max (succ u5) (succ u6), succ u5, succ u6} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u2, succ u7} (Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) ι₁ (fun (a : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => M) a) (Basis.funLike.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) (FunLike.coe.{max (max (succ u7) (succ u5)) (succ u6), succ u7, max (succ u5) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) 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_inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _x) (LinearMap.instFunLikeLinearMap.{u9, u8, u7, max u5 u6} R R₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
@@ -79,7 +79,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {Mₗ : Type.{u4}} {Nₗ : Type.{u5}} {Pₗ : Type.{u6}} [_inst_1 : CommSemiring.{u3} R] [_inst_8 : AddCommMonoid.{u4} Mₗ] [_inst_9 : AddCommMonoid.{u5} Nₗ] [_inst_10 : AddCommMonoid.{u6} Pₗ] [_inst_15 : Module.{u3, u4} R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8] [_inst_16 : Module.{u3, u5} R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9] [_inst_17 : Module.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10] (b₁' : Basis.{u1, u3, u4} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u3, u3, u4, max u5 u6} 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))) Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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_inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17))))) => Mₗ -> (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17)) (LinearMap.hasCoeToFun.{u3, u3, u4, max u5 u6} R R Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) B x) y)
 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R 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ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) 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_inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) x) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Nₗ) => Pₗ) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (FunLike.coe.{max (max (succ u5) (succ u3)) (succ u4), succ u5, max (succ u3) (succ u4)} (LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Mₗ) => LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u5, max u3 u4} R R Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B x) y)
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R 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(CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u5} R Mₗ (AddMonoid.toZero.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribSMul.toSMulZeroClass.{u6, u5} R Mₗ (AddMonoid.toAddZeroClass.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribMulAction.toDistribSMul.{u6, u5} R Mₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15)))) (SMulZeroClass.toSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R 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(Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) 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(CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

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

@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u3, u4, u7, max u8 u9} R R₂ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) ρ₁₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u9} P (Finsupp.sum.{u1, u3, u9} ι₁ R P (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_7 (coeFn.{max (succ u7) (succ (max u1 u3)), max (succ u7) (succ (max u1 u3))} (LinearEquiv.{u3, u3, u7, 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} ι₁ R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_5 (Finsupp.addCommMonoid.{u1, u3} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_11 (Finsupp.module.{u1, u3, u3} ι₁ 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, u7, 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} ι₁ R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R 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 but is expected to have type
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(RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S 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(Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S 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(CommSemiring.toSemiring.{u4} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))))) σ₁₂ yj) (FunLike.coe.{max (succ u5) (succ u6), succ u5, succ u6} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u2, succ u7} (Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) ι₁ (fun (a : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => M) a) (Basis.funLike.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) (FunLike.coe.{max (max (succ u7) (succ u5)) (succ u6), succ u7, max (succ u5) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) 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_inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -49,7 +49,7 @@ variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 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(CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₂) => N) _x) (Basis.funLike.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) b₂ j))) -> (Eq.{max (max (succ u7) (succ u5)) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) B B')
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u3, u4, u7, max u8 u9} R R₂ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) ρ₁₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u9} P (Finsupp.sum.{u1, u3, u9} ι₁ R P (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R 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(CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)) => M -> (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14)) (LinearMap.hasCoeToFun.{u3, u4, u7, max u8 u9} R R₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (SMulZeroClass.toSMul.{u9, u7} R M (AddMonoid.toZero.{u7} M (AddCommMonoid.toAddMonoid.{u7} M _inst_5)) (DistribSMul.toSMulZeroClass.{u9, u7} R M (AddMonoid.toAddZeroClass.{u7} M (AddCommMonoid.toAddMonoid.{u7} M _inst_5)) (DistribMulAction.toDistribSMul.{u9, u7} R M (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11)))) (SMulZeroClass.toSMul.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddMonoid.toZero.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R 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_inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} 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_inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (SMulZeroClass.toSMul.{u9, u7} R M (AddMonoid.toZero.{u7} M (AddCommMonoid.toAddMonoid.{u7} M _inst_5)) (DistribSMul.toSMulZeroClass.{u9, u7} R M (AddMonoid.toAddZeroClass.{u7} M (AddCommMonoid.toAddMonoid.{u7} M _inst_5)) (DistribMulAction.toDistribSMul.{u9, u7} R M (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11)))) (SMulZeroClass.toSMul.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u9, u7, max u2 u9, max (max u2 u9) u7} R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S 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 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
@@ -79,7 +79,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {Mₗ : Type.{u4}} {Nₗ : Type.{u5}} {Pₗ : Type.{u6}} [_inst_1 : CommSemiring.{u3} R] [_inst_8 : AddCommMonoid.{u4} Mₗ] [_inst_9 : AddCommMonoid.{u5} Nₗ] [_inst_10 : AddCommMonoid.{u6} Pₗ] [_inst_15 : Module.{u3, u4} R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8] [_inst_16 : Module.{u3, u5} R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9] [_inst_17 : Module.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10] (b₁' : Basis.{u1, u3, u4} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u3, u3, u4, max u5 u6} 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))) Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u6} Pₗ (Finsupp.sum.{u1, u3, u6} ι₁ R Pₗ (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_10 (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} 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) => Mₗ -> (Finsupp.{u1, u3} ι₁ 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 Mₗ (Finsupp.{u1, u3} ι₁ 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_8 (Finsupp.addCommMonoid.{u1, u3} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_15 (Finsupp.module.{u1, u3, u3} ι₁ 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} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u2, u3, u6} ι₂ R Pₗ (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R 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(LinearEquiv.hasCoeToFun.{u3, u3, u5, max u2 u3} R R Nₗ (Finsupp.{u2, u3} ι₂ 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_9 (Finsupp.addCommMonoid.{u2, u3} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_16 (Finsupp.module.{u2, u3, u3} ι₂ 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.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16 b₂') y) (fun (j : ι₂) (yj : R) => SMul.smul.{u3, u6} R Pₗ (SMulZeroClass.toHasSmul.{u3, u6} R Pₗ (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (SMulWithZero.toSmulZeroClass.{u3, u6} R Pₗ (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (MulActionWithZero.toSMulWithZero.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) xi (SMul.smul.{u3, u6} R Pₗ (SMulZeroClass.toHasSmul.{u3, u6} R Pₗ (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (SMulWithZero.toSmulZeroClass.{u3, u6} R Pₗ (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (MulActionWithZero.toSMulWithZero.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) yj (coeFn.{max (succ u5) (succ u6), max (succ u5) (succ u6)} (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (fun (_x : LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) => Nₗ -> Pₗ) (LinearMap.hasCoeToFun.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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_inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17))))) => Mₗ -> (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17)) (LinearMap.hasCoeToFun.{u3, u3, u4, max u5 u6} R R Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) B x) y)
 but is expected to have type
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(Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R 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ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R 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(CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R 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(Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) (Module.toDistribMulAction.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u3, max u1 u6, max (max u1 u6) u3} R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R 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_inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u2, succ u5} (Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) ι₁ (fun (_x : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => Mₗ) _x) (Basis.funLike.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) b₁' i)) (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u1, succ u3} (Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₂) => Nₗ) _x) (Basis.funLike.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) b₂' j)))))) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Mₗ) => LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) x) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Nₗ) => Pₗ) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (FunLike.coe.{max (max (succ u5) (succ u3)) (succ u4), succ u5, max (succ u3) (succ u4)} (LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Mₗ) => LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u5, max u3 u4} R R Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B x) y)
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R 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ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) 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B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -49,7 +49,7 @@ variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 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(CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₂) => N) _x) (Basis.funLike.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) b₂ j))) -> (Eq.{max (max (succ u7) (succ u5)) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) B B')
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u3, u4, u7, max u8 u9} R R₂ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) ρ₁₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u9} P (Finsupp.sum.{u1, u3, u9} ι₁ R P (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R 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 but is expected to have type
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_inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R 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_inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddMonoid.toZero.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddMonoid.toAddZeroClass.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S 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(RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} 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(AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) 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(_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => S₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))))) σ₁₂ yj) (FunLike.coe.{max (succ u5) (succ u6), succ u5, succ u6} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u2, succ u7} (Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) ι₁ (fun (a : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => M) a) (Basis.funLike.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) (FunLike.coe.{max (max (succ u7) (succ u5)) (succ u6), succ u7, max (succ u5) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) 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_inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _x) (LinearMap.instFunLikeLinearMap.{u9, u8, u7, max u5 u6} R R₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
@@ -79,7 +79,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {Mₗ : Type.{u4}} {Nₗ : Type.{u5}} {Pₗ : Type.{u6}} [_inst_1 : CommSemiring.{u3} R] [_inst_8 : AddCommMonoid.{u4} Mₗ] [_inst_9 : AddCommMonoid.{u5} Nₗ] [_inst_10 : AddCommMonoid.{u6} Pₗ] [_inst_15 : Module.{u3, u4} R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8] [_inst_16 : Module.{u3, u5} R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9] [_inst_17 : Module.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10] (b₁' : Basis.{u1, u3, u4} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u3, u3, u4, max u5 u6} 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))) Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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_inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17))))) => Mₗ -> (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17)) (LinearMap.hasCoeToFun.{u3, u3, u4, max u5 u6} R R Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) B x) y)
 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R 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ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) 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_inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) x) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Nₗ) => Pₗ) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (FunLike.coe.{max (max (succ u5) (succ u3)) (succ u4), succ u5, max (succ u3) (succ u4)} (LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Mₗ) => LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u5, max u3 u4} R R Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B x) y)
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R 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(CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u5} R Mₗ (AddMonoid.toZero.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribSMul.toSMulZeroClass.{u6, u5} R Mₗ (AddMonoid.toAddZeroClass.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribMulAction.toDistribSMul.{u6, u5} R Mₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15)))) (SMulZeroClass.toSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) 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(CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

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

@@ -49,7 +49,7 @@ variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 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+  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u1, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} {B' : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)}, (forall (i : ι₁) (j : ι₂), Eq.{succ u6} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) ι₂ (fun (a : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι₂) => N) a) (Basis.funLike.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) b₂ j)) (FunLike.coe.{max (succ u5) (succ u6), succ u5, succ u6} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (FunLike.coe.{max (max (succ u1) (succ u9)) (succ u7), succ u1, succ u7} (Basis.{u1, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) ι₁ (fun (a : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι₁) => M) a) (Basis.funLike.{u1, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) (FunLike.coe.{max (max (succ u7) (succ u5)) (succ u6), succ u7, max (succ u5) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 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(CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) (FunLike.coe.{max (max (succ u2) (succ u4)) (succ u5), succ u2, succ u5} (Basis.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι₂) => N) _x) (Basis.funLike.{u2, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) b₂ j))) -> (Eq.{max (max (succ u7) (succ u5)) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) B B')
 Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u3, u4, u7, max u8 u9} R R₂ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) ρ₁₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u9} P (Finsupp.sum.{u1, u3, u9} ι₁ R P (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R 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 but is expected to have type
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(CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u9) u7, u9, u7, max u2 u9} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 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(CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u9) u7, u9, u7, max u2 u9} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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_inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _x) (LinearMap.instFunLikeLinearMap.{u9, u8, u7, max u5 u6} R R₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S 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 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
@@ -79,7 +79,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {Mₗ : Type.{u4}} {Nₗ : Type.{u5}} {Pₗ : Type.{u6}} [_inst_1 : CommSemiring.{u3} R] [_inst_8 : AddCommMonoid.{u4} Mₗ] [_inst_9 : AddCommMonoid.{u5} Nₗ] [_inst_10 : AddCommMonoid.{u6} Pₗ] [_inst_15 : Module.{u3, u4} R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8] [_inst_16 : Module.{u3, u5} R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9] [_inst_17 : Module.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10] (b₁' : Basis.{u1, u3, u4} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u3, u3, u4, max u5 u6} 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))) Mₗ (LinearMap.{u3, u3, u5, u6} R R (CommSemiring.toSemiring.{u3} R _inst_1) 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_inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17))))) => Mₗ -> (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17)) (LinearMap.hasCoeToFun.{u3, u3, u4, max u5 u6} R R Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) B x) y)
 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u5} R Mₗ (AddMonoid.toZero.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribSMul.toSMulZeroClass.{u6, u5} R Mₗ (AddMonoid.toAddZeroClass.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribMulAction.toDistribSMul.{u6, u5} R Mₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15)))) (SMulZeroClass.toSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R 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B x) y)
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u5} R Mₗ (AddMonoid.toZero.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribSMul.toSMulZeroClass.{u6, u5} R Mₗ (AddMonoid.toAddZeroClass.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribMulAction.toDistribSMul.{u6, u5} R Mₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15)))) (SMulZeroClass.toSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) (Module.toDistribMulAction.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u3, max u1 u6, max (max u1 u6) u3} R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u3, max u1 u6, max (max u1 u6) u3} R R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R 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B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

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

@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 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 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ 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RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 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(CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u9, u7, max u2 u9, max (max u2 u9) u7} R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 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(CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u9, u7, max u2 u9, max (max u2 u9) u7} R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) 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(CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) 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_inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _x) (LinearMap.instFunLikeLinearMap.{u9, u8, u7, max u5 u6} R R₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -61,7 +61,7 @@ theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : 
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ (MulZeroOneClass.toMulZeroClass.{u6} S₂ (MonoidWithZero.toMulZeroOneClass.{u6} S₂ (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u6, u9} S₂ P (Semiring.toMonoidWithZero.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toHasSmul.{u4, u9} R₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u4, u9} R₂ P (MulZeroClass.toHasZero.{u4} R₂ (MulZeroOneClass.toMulZeroClass.{u4} R₂ (MonoidWithZero.toMulZeroOneClass.{u4} R₂ (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))))) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (MulActionWithZero.toSMulWithZero.{u4, u9} R₂ P (Semiring.toMonoidWithZero.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3)) (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (Module.toMulActionWithZero.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u3, u4} R R₂ (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} R₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3))} {σ₁₂ : RingHom.{u5, u6} S S₂ (Semiring.toNonAssocSemiring.{u5} S (CommSemiring.toSemiring.{u5} S _inst_2)) (Semiring.toNonAssocSemiring.{u6} S₂ (CommSemiring.toSemiring.{u6} S₂ _inst_4))} (b₁ : Basis.{u1, u3, u7} ι₁ R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u2, u5, u8} ι₂ S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u3, u4, u7, max u8 u9} R R₂ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} R₂ _inst_3) ρ₁₂ M (LinearMap.{u5, u6, u8, u9} S S₂ (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u5, u6, u8, u9} S S₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.module.{u5, u6, u4, u8, u9} S S₂ R₂ N P (CommSemiring.toSemiring.{u5} S _inst_2) (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u9} P (Finsupp.sum.{u1, u3, u9} ι₁ R P (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) _inst_7 (coeFn.{max (succ u7) (succ (max u1 u3)), max (succ u7) (succ (max u1 u3))} (LinearEquiv.{u3, u3, u7, 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} ι₁ R (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) _inst_5 (Finsupp.addCommMonoid.{u1, u3} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R 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 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max 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(MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S 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+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u9) u7, u9, u7, max u2 u9} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (SMulZeroClass.toSMul.{u9, u7} R M (AddMonoid.toZero.{u7} M (AddCommMonoid.toAddMonoid.{u7} M _inst_5)) (DistribSMul.toSMulZeroClass.{u9, u7} R M (AddMonoid.toAddZeroClass.{u7} M (AddCommMonoid.toAddMonoid.{u7} M _inst_5)) (DistribMulAction.toDistribSMul.{u9, u7} R M (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11)))) (SMulZeroClass.toSMul.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddMonoid.toZero.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, 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(CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (MonoidWithZero.toMonoid.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (AddCommMonoid.toAddMonoid.{u7} M _inst_5) (AddCommMonoid.toAddMonoid.{max u2 u9} (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))))) (Module.toDistribMulAction.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (Module.toDistribMulAction.{u9, max u2 u9} R (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R 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(Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u9, u9, u7, max u2 u9, max (max u2 u9) u7} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u9, u9, u7, max u2 u9} R R M (Finsupp.{u2, u9} ι₁ R (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 (Finsupp.addCommMonoid.{u2, u9} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))) _inst_11 (Finsupp.module.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u4)) (succ u5), succ u5, max (succ u1) (succ u4)} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : N) => Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _x) (SMulHomClass.toFunLike.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SMulZeroClass.toSMul.{u4, u5} S N (AddMonoid.toZero.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribSMul.toSMulZeroClass.{u4, u5} S N (AddMonoid.toAddZeroClass.{u5} N (AddCommMonoid.toAddMonoid.{u5} N _inst_6)) (DistribMulAction.toDistribSMul.{u4, u5} S N (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12)))) (SMulZeroClass.toSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddMonoid.toZero.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribSMul.toSMulZeroClass.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddMonoid.toAddZeroClass.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulAction.toDistribSMul.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u4) u5, u4, u5, max u1 u4} (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.module.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u5, max u1 u4, max (max u1 u4) u5} S S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) 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(_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : S) => S₂) _x) (MulHomClass.toFunLike.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (NonUnitalNonAssocSemiring.toMul.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u3} S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S₂ (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u3, u4, u3} (RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))) S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (RingHom.instRingHomClassRingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)))))) σ₁₂ yj) (FunLike.coe.{max (succ u5) (succ u6), succ u5, succ u6} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u2, succ u7} (Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) ι₁ (fun (a : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι₁) => M) a) (Basis.funLike.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) b₁ i)) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : N) => P) _x) (LinearMap.instFunLikeLinearMap.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) (FunLike.coe.{max (max (succ u7) (succ u5)) (succ u6), succ u7, max (succ u5) (succ u6)} (LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) 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_inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _x) (LinearMap.instFunLikeLinearMap.{u9, u8, u7, max u5 u6} R R₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18) ρ₁₂) B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
@@ -79,7 +79,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 lean 3 declaration is
   forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {Mₗ : Type.{u4}} {Nₗ : Type.{u5}} {Pₗ : Type.{u6}} [_inst_1 : CommSemiring.{u3} R] [_inst_8 : AddCommMonoid.{u4} Mₗ] [_inst_9 : AddCommMonoid.{u5} Nₗ] [_inst_10 : AddCommMonoid.{u6} Pₗ] [_inst_15 : Module.{u3, u4} R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8] [_inst_16 : Module.{u3, u5} R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9] [_inst_17 : Module.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10] (b₁' : Basis.{u1, u3, u4} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u3, u3, u4, max u5 u6} 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))) Mₗ (LinearMap.{u3, u3, u5, u6} R R (CommSemiring.toSemiring.{u3} R _inst_1) 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_inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17))))) => Mₗ -> (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17)) (LinearMap.hasCoeToFun.{u3, u3, u4, max u5 u6} R R Mₗ (LinearMap.{u3, u3, u5, u6} 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))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u3, u3, u5, u6} R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) _inst_15 (LinearMap.module.{u3, u3, u3, u5, u6} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (CommSemiring.toSemiring.{u3} R _inst_1) _inst_17 (smulCommClass_self.{u3, u6} R Pₗ (CommSemiring.toCommMonoid.{u3} R _inst_1) (MulActionWithZero.toMulAction.{u3, u6} R Pₗ (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (Module.toMulActionWithZero.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) B x) y)
 but is expected to have type
-  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) 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(CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, 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ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) ι₁ (fun (_x : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι₁) => Mₗ) _x) (Basis.funLike.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) b₁' i)) (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u1, succ u3} (Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) ι₂ (fun (_x : ι₂) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι₂) => Nₗ) _x) (Basis.funLike.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) b₂' j)))))) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Mₗ) => LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) x) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Nₗ) => Pₗ) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (FunLike.coe.{max (max (succ u5) (succ u3)) (succ u4), succ u5, max (succ u3) (succ u4)} (LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : Mₗ) => LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _x) (LinearMap.instFunLikeLinearMap.{u6, u6, u5, max u3 u4} R R Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17)))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) B x) y)
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Nₗ Pₗ _inst_9 _inst_10 _inst_16 _inst_17) _inst_8 (LinearMap.addCommMonoid.{u6, u6, u3, u4} R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_15 (LinearMap.instModuleLinearMapAddCommMonoid.{u6, u6, u6, u3, u4} R R R Nₗ Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_10 _inst_16 _inst_17 (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_17 (smulCommClass_self.{u6, u4} R Pₗ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R Pₗ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} Pₗ (AddCommMonoid.toAddMonoid.{u4} Pₗ _inst_10)) (Module.toMulActionWithZero.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10 _inst_17))))} (x : Mₗ) (y : Nₗ), Eq.{succ u4} Pₗ (Finsupp.sum.{u2, u6, u4} ι₁ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u2) (succ u6)) (succ u5), succ u5, max (succ u2) (succ u6)} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Mₗ (fun (_x : Mₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Mₗ) => Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R 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(CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u5} R Mₗ (AddMonoid.toZero.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribSMul.toSMulZeroClass.{u6, u5} R Mₗ (AddMonoid.toAddZeroClass.{u5} Mₗ (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8)) (DistribMulAction.toDistribSMul.{u6, u5} R Mₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15)))) (SMulZeroClass.toSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u2 u6} (Finsupp.{u2, u6} 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(CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u6) u5, u6, u5, max u2 u6} (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u5} Mₗ _inst_8) (AddCommMonoid.toAddMonoid.{max u2 u6} (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))))) (Module.toDistribMulAction.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (Module.toDistribMulAction.{u6, max u2 u6} R (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SemilinearMapClass.distribMulActionHomClass.{u6, u5, max u2 u6, max (max u2 u6) u5} R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u6, u6, u5, max u2 u6, max (max u2 u6) u5} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (LinearEquiv.{u6, u6, u5, max u6 u2} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u6, u6, u5, max u2 u6} R R Mₗ (Finsupp.{u2, u6} ι₁ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.module.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (Basis.repr.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15 b₁') x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u6, u4} ι₂ R Pₗ (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) _inst_10 (FunLike.coe.{max (max (succ u1) (succ u6)) (succ u3), succ u3, max (succ u1) (succ u6)} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) Nₗ (fun (_x : Nₗ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Nₗ) => Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max u1 u6) u3, u6, u3, max u1 u6} (LinearEquiv.{u6, u6, u3, max u6 u1} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (RingHomInvPair.ids.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.module.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (SMulZeroClass.toSMul.{u6, u3} R Nₗ (AddMonoid.toZero.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribSMul.toSMulZeroClass.{u6, u3} R Nₗ (AddMonoid.toAddZeroClass.{u3} Nₗ (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9)) (DistribMulAction.toDistribSMul.{u6, u3} R Nₗ (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ _inst_9) (Module.toDistribMulAction.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16)))) (SMulZeroClass.toSMul.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toZero.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u6, max u1 u6} R (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u6} (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R 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B x) y)
 Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module linear_algebra.basis.bilinear
-! leanprover-community/mathlib commit 87c54600fe3cdc7d32ff5b50873ac724d86aef8d
+! leanprover-community/mathlib commit 832f7b9162039c28b9361289c8681f155cae758f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.BilinearMap
 
 /-!
 # Lemmas about bilinear maps with a basis over each argument
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -42,12 +42,24 @@ variable {ρ₁₂ : R →+* R₂} {σ₁₂ : S →+* S₂}
 
 variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ R Mₗ) (b₂' : Basis ι₂ R Nₗ)
 
+/- warning: linear_map.ext_basis -> LinearMap.ext_basis is a dubious translation:
+lean 3 declaration is
+  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {R₂ : Type.{u4}} {S : Type.{u5}} {S₂ : Type.{u6}} {M : Type.{u7}} {N : Type.{u8}} {P : Type.{u9}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u5} S] [_inst_3 : CommSemiring.{u4} R₂] [_inst_4 : CommSemiring.{u6} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : AddCommMonoid.{u9} P] [_inst_11 : Module.{u3, u7} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_5] [_inst_12 : Module.{u5, u8} S N (CommSemiring.toSemiring.{u5} S _inst_2) _inst_6] [_inst_13 : Module.{u4, u9} R₂ P (CommSemiring.toSemiring.{u4} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u6, u9} S₂ P (CommSemiring.toSemiring.{u6} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u6, u4, u9} S₂ R₂ P (SMulZeroClass.toHasSmul.{u6, u9} S₂ P (AddZeroClass.toHasZero.{u9} P (AddMonoid.toAddZeroClass.{u9} P (AddCommMonoid.toAddMonoid.{u9} P _inst_7))) (SMulWithZero.toSmulZeroClass.{u6, u9} S₂ P (MulZeroClass.toHasZero.{u6} S₂ 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+Case conversion may be inaccurate. Consider using '#align linear_map.ext_basis LinearMap.ext_basisₓ'. -/
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
     B = B' :=
   b₁.ext fun i => b₂.ext fun j => h i j
 #align linear_map.ext_basis LinearMap.ext_basis
 
+/- warning: linear_map.sum_repr_mul_repr_mulₛₗ -> LinearMap.sum_repr_mul_repr_mulₛₗ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u9}} {R₂ : Type.{u8}} {S : Type.{u4}} {S₂ : Type.{u3}} {M : Type.{u7}} {N : Type.{u5}} {P : Type.{u6}} [_inst_1 : CommSemiring.{u9} R] [_inst_2 : CommSemiring.{u4} S] [_inst_3 : CommSemiring.{u8} R₂] [_inst_4 : CommSemiring.{u3} S₂] [_inst_5 : AddCommMonoid.{u7} M] [_inst_6 : AddCommMonoid.{u5} N] [_inst_7 : AddCommMonoid.{u6} P] [_inst_11 : Module.{u9, u7} R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5] [_inst_12 : Module.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6] [_inst_13 : Module.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7] [_inst_14 : Module.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7] [_inst_18 : SMulCommClass.{u3, u8, u6} S₂ R₂ P (SMulZeroClass.toSMul.{u3, u6} S₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u3, u6} S₂ P (CommMonoidWithZero.toZero.{u3} S₂ (CommSemiring.toCommMonoidWithZero.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u3, u6} S₂ P (Semiring.toMonoidWithZero.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u3, u6} S₂ P (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_7 _inst_14)))) (SMulZeroClass.toSMul.{u8, u6} R₂ P (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (SMulWithZero.toSMulZeroClass.{u8, u6} R₂ P (CommMonoidWithZero.toZero.{u8} R₂ (CommSemiring.toCommMonoidWithZero.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (MulActionWithZero.toSMulWithZero.{u8, u6} R₂ P (Semiring.toMonoidWithZero.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3)) (AddMonoid.toZero.{u6} P (AddCommMonoid.toAddMonoid.{u6} P _inst_7)) (Module.toMulActionWithZero.{u8, u6} R₂ P (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_7 _inst_13))))] {ρ₁₂ : RingHom.{u9, u8} R R₂ (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (Semiring.toNonAssocSemiring.{u8} R₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3))} {σ₁₂ : RingHom.{u4, u3} S S₂ (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (Semiring.toNonAssocSemiring.{u3} S₂ (CommSemiring.toSemiring.{u3} S₂ _inst_4))} (b₁ : Basis.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11) (b₂ : Basis.{u1, u4, u5} ι₂ S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) {B : LinearMap.{u9, u8, u7, max u6 u5} R R₂ (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u8} R₂ _inst_3) ρ₁₂ M (LinearMap.{u4, u3, u5, u6} S S₂ (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) σ₁₂ N P _inst_6 _inst_7 _inst_12 _inst_14) _inst_5 (LinearMap.addCommMonoid.{u4, u3, u5, u6} S S₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂) _inst_11 (LinearMap.instModuleLinearMapAddCommMonoid.{u4, u3, u8, u5, u6} S S₂ R₂ N P (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u3} S₂ _inst_4) _inst_6 _inst_7 _inst_12 _inst_14 σ₁₂ (CommSemiring.toSemiring.{u8} R₂ _inst_3) _inst_13 _inst_18)} (x : M) (y : N), Eq.{succ u6} P (Finsupp.sum.{u2, u9, u6} ι₁ R P (MonoidWithZero.toZero.{u9} R (Semiring.toMonoidWithZero.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) _inst_7 (FunLike.coe.{max (max (succ u2) (succ u9)) (succ u7), succ u7, max (succ u2) (succ u9)} (LinearEquiv.{u9, u9, u7, max u9 u2} R R (CommSemiring.toSemiring.{u9} R _inst_1) (CommSemiring.toSemiring.{u9} R _inst_1) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u9, u9} ι₁ R R (CommSemiring.toSemiring.{u9} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u9} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)))) (Semiring.toModule.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHom.id.{u9} R (Semiring.toNonAssocSemiring.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1)) (RingHomInvPair.ids.{u9} R (CommSemiring.toSemiring.{u9} R _inst_1))))))) (Basis.repr.{u2, u9, u7} ι₁ R M (CommSemiring.toSemiring.{u9} R _inst_1) _inst_5 _inst_11 b₁) x) (fun (i : ι₁) (xi : R) => Finsupp.sum.{u1, u4, u6} ι₂ S P (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) _inst_7 (FunLike.coe.{max 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(MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (MonoidWithZero.toMonoid.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (AddCommMonoid.toAddMonoid.{u5} N _inst_6) (AddCommMonoid.toAddMonoid.{max u1 u4} (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))))) (Module.toDistribMulAction.{u4, u5} S N (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 _inst_12) (Module.toDistribMulAction.{u4, max u1 u4} S (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (SemilinearMapClass.distribMulActionHomClass.{u4, u5, max u1 u4, max (max u1 u4) u5} S N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (LinearEquiv.{u4, u4, u5, max u4 u1} S S (CommSemiring.toSemiring.{u4} S _inst_2) (CommSemiring.toSemiring.{u4} S _inst_2) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHom.id.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) (RingHomInvPair.ids.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)) N (Finsupp.{u1, u4} ι₂ S (MonoidWithZero.toZero.{u4} S (Semiring.toMonoidWithZero.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2))))) _inst_12 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u4, u4} ι₂ S S (CommSemiring.toSemiring.{u4} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (Semiring.toModule.{u4} S (CommSemiring.toSemiring.{u4} S _inst_2)))) (CommSemiring.toSemiring.{u4} S _inst_2) _inst_6 (Finsupp.addCommMonoid.{u1, u4} ι₂ S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} S (Semiring.toNonAssocSemiring.{u4} S (CommSemiring.toSemiring.{u4} S 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+Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for semi-bilinear maps, see `sum_repr_mul_repr_mul` for the bilinear version. -/
@@ -60,6 +72,12 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
     LinearMap.map_smulₛₗ]
 #align linear_map.sum_repr_mul_repr_mulₛₗ LinearMap.sum_repr_mul_repr_mulₛₗ
 
+/- warning: linear_map.sum_repr_mul_repr_mul -> LinearMap.sum_repr_mul_repr_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι₁ : Type.{u1}} {ι₂ : Type.{u2}} {R : Type.{u3}} {Mₗ : Type.{u4}} {Nₗ : Type.{u5}} {Pₗ : Type.{u6}} [_inst_1 : CommSemiring.{u3} R] [_inst_8 : AddCommMonoid.{u4} Mₗ] [_inst_9 : AddCommMonoid.{u5} Nₗ] [_inst_10 : AddCommMonoid.{u6} Pₗ] [_inst_15 : Module.{u3, u4} R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8] [_inst_16 : Module.{u3, u5} R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9] [_inst_17 : Module.{u3, u6} R Pₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_10] (b₁' : Basis.{u1, u3, u4} ι₁ R Mₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u3, u3, u4, max u5 u6} 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))) Mₗ (LinearMap.{u3, u3, u5, u6} R R (CommSemiring.toSemiring.{u3} R _inst_1) 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(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.{u2, u3, u5} ι₂ R Nₗ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_9 _inst_16 b₂') y) (fun (j : ι₂) (yj : R) => SMul.smul.{u3, u6} R Pₗ (SMulZeroClass.toHasSmul.{u3, u6} R Pₗ (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (SMulWithZero.toSmulZeroClass.{u3, u6} R Pₗ (MulZeroClass.toHasZero.{u3} R (MulZeroOneClass.toMulZeroClass.{u3} R (MonoidWithZero.toMulZeroOneClass.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (AddZeroClass.toHasZero.{u6} Pₗ (AddMonoid.toAddZeroClass.{u6} Pₗ (AddCommMonoid.toAddMonoid.{u6} Pₗ _inst_10))) (MulActionWithZero.toSMulWithZero.{u3, u6} R Pₗ 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+but is expected to have type
+  forall {ι₁ : Type.{u2}} {ι₂ : Type.{u1}} {R : Type.{u6}} {Mₗ : Type.{u5}} {Nₗ : Type.{u3}} {Pₗ : Type.{u4}} [_inst_1 : CommSemiring.{u6} R] [_inst_8 : AddCommMonoid.{u5} Mₗ] [_inst_9 : AddCommMonoid.{u3} Nₗ] [_inst_10 : AddCommMonoid.{u4} Pₗ] [_inst_15 : Module.{u6, u5} R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8] [_inst_16 : Module.{u6, u3} R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9] [_inst_17 : Module.{u6, u4} R Pₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_10] (b₁' : Basis.{u2, u6, u5} ι₁ R Mₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 _inst_15) (b₂' : Basis.{u1, u6, u3} ι₂ R Nₗ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 _inst_16) {B : LinearMap.{u6, u6, u5, max u4 u3} R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) Mₗ (LinearMap.{u6, u6, u3, u4} R R (CommSemiring.toSemiring.{u6} R _inst_1) 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(Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_8 (Finsupp.addCommMonoid.{u2, u6} ι₁ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_15 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u2, u6, u6} ι₁ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) 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(MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) R Nₗ (Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MonoidWithZero.toMonoid.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} Nₗ 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(Finsupp.{u1, u6} ι₂ R (MonoidWithZero.toZero.{u6} R (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1))))) _inst_16 (Finsupp.instModuleFinsuppToZeroToAddMonoidAddCommMonoid.{u1, u6, u6} ι₂ R R (CommSemiring.toSemiring.{u6} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (Semiring.toModule.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (CommSemiring.toSemiring.{u6} R _inst_1) _inst_9 (Finsupp.addCommMonoid.{u1, u6} ι₂ R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u6} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R 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+Case conversion may be inaccurate. Consider using '#align linear_map.sum_repr_mul_repr_mul LinearMap.sum_repr_mul_repr_mulₓ'. -/
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for bilinear maps, see `sum_repr_mul_repr_mulₛₗ` for the semi-bilinear version. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

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)

@@ -16,9 +16,7 @@ import Mathlib.LinearAlgebra.BilinearMap
 namespace LinearMap
 
 variable {ι₁ ι₂ : Type*}
-
 variable {R R₂ S S₂ M N P Rₗ : Type*}
-
 variable {Mₗ Nₗ Pₗ : Type*}
 
 -- Could weaken [CommSemiring Rₗ] to [SMulCommClass Rₗ Rₗ Pₗ], but might impact performance
@@ -27,17 +25,11 @@ variable [Semiring R] [Semiring S] [Semiring R₂] [Semiring S₂] [CommSemiring
 section AddCommMonoid
 
 variable [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P]
-
 variable [AddCommMonoid Mₗ] [AddCommMonoid Nₗ] [AddCommMonoid Pₗ]
-
 variable [Module R M] [Module S N] [Module R₂ P] [Module S₂ P]
-
 variable [Module Rₗ Mₗ] [Module Rₗ Nₗ] [Module Rₗ Pₗ]
-
 variable [SMulCommClass S₂ R₂ P]
-
 variable {ρ₁₂ : R →+* R₂} {σ₁₂ : S →+* S₂}
-
 variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ Rₗ Mₗ) (b₂' : Basis ι₂ Rₗ Nₗ)
 
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/

Remove unused commutativity hypothesis:

• Removes the requirement for the Semirings to be commutative in LinearMap.ext_basis and LinearMap.sum_repr_mul_repr_mulₛₗ in LinearAlgebra/Basis/Bilinear
• Remove the requirement for some Semirings to be commutative in AuxToLinearMap, CommSemiring and CommRing in LinearAlgebra/Matrix/SesquilinearForm
• In addition, the rings in CommRing can just be Semiring

No changes to the proofs are required.

It would also be possible to weaken commutativity from Rₗ in LinearMap.sum_repr_mul_repr_mul to [SMulCommClass Rₗ Rₗ Pₗ] in order to make sum_repr_mul_repr_mulₛₗ and sum_repr_mul_repr_mul consistent, but I have not done that in this PR because there might be a performance impact (see https://github.com/leanprover-community/mathlib4/pull/7538#pullrequestreview-1663000126).

Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>

@@ -17,11 +17,12 @@ namespace LinearMap
 
 variable {ι₁ ι₂ : Type*}
 
-variable {R R₂ S S₂ M N P : Type*}
+variable {R R₂ S S₂ M N P Rₗ : Type*}
 
 variable {Mₗ Nₗ Pₗ : Type*}
 
-variable [CommSemiring R] [CommSemiring S] [CommSemiring R₂] [CommSemiring S₂]
+-- Could weaken [CommSemiring Rₗ] to [SMulCommClass Rₗ Rₗ Pₗ], but might impact performance
+variable [Semiring R] [Semiring S] [Semiring R₂] [Semiring S₂] [CommSemiring Rₗ]
 
 section AddCommMonoid
 
@@ -31,13 +32,13 @@ variable [AddCommMonoid Mₗ] [AddCommMonoid Nₗ] [AddCommMonoid Pₗ]
 
 variable [Module R M] [Module S N] [Module R₂ P] [Module S₂ P]
 
-variable [Module R Mₗ] [Module R Nₗ] [Module R Pₗ]
+variable [Module Rₗ Mₗ] [Module Rₗ Nₗ] [Module Rₗ Pₗ]
 
 variable [SMulCommClass S₂ R₂ P]
 
 variable {ρ₁₂ : R →+* R₂} {σ₁₂ : S →+* S₂}
 
-variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ R Mₗ) (b₂' : Basis ι₂ R Nₗ)
+variable (b₁ : Basis ι₁ R M) (b₂ : Basis ι₂ S N) (b₁' : Basis ι₁ Rₗ Mₗ) (b₂' : Basis ι₂ Rₗ Nₗ)
 
 /-- Two bilinear maps are equal when they are equal on all basis vectors. -/
 theorem ext_basis {B B' : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂] P} (h : ∀ i j, B (b₁ i) (b₂ j) = B' (b₁ i) (b₂ j)) :
@@ -59,7 +60,7 @@ theorem sum_repr_mul_repr_mulₛₗ {B : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁
 /-- Write out `B x y` as a sum over `B (b i) (b j)` if `b` is a basis.
 
 Version for bilinear maps, see `sum_repr_mul_repr_mulₛₗ` for the semi-bilinear version. -/
-theorem sum_repr_mul_repr_mul {B : Mₗ →ₗ[R] Nₗ →ₗ[R] Pₗ} (x y) :
+theorem sum_repr_mul_repr_mul {B : Mₗ →ₗ[Rₗ] Nₗ →ₗ[Rₗ] Pₗ} (x y) :
     ((b₁'.repr x).sum fun i xi => (b₂'.repr y).sum fun j yj => xi • yj • B (b₁' i) (b₂' j)) =
       B x y := by
   conv_rhs => rw [← b₁'.total_repr x, ← b₂'.total_repr y]
@@ -70,4 +71,3 @@ theorem sum_repr_mul_repr_mul {B : Mₗ →ₗ[R] Nₗ →ₗ[R] Pₗ} (x y) :
 end AddCommMonoid
 
 end LinearMap
-

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

This has nice performance benefits.

@@ -15,11 +15,11 @@ import Mathlib.LinearAlgebra.BilinearMap
 
 namespace LinearMap
 
-variable {ι₁ ι₂ : Type _}
+variable {ι₁ ι₂ : Type*}
 
-variable {R R₂ S S₂ M N P : Type _}
+variable {R R₂ S S₂ M N P : Type*}
 
-variable {Mₗ Nₗ Pₗ : Type _}
+variable {Mₗ Nₗ Pₗ : Type*}
 
 variable [CommSemiring R] [CommSemiring S] [CommSemiring R₂] [CommSemiring S₂]
 

• 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) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module linear_algebra.basis.bilinear
-! leanprover-community/mathlib commit 87c54600fe3cdc7d32ff5b50873ac724d86aef8d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Basis
 import Mathlib.LinearAlgebra.BilinearMap
 
+#align_import linear_algebra.basis.bilinear from "leanprover-community/mathlib"@"87c54600fe3cdc7d32ff5b50873ac724d86aef8d"
+
 /-!
 # Lemmas about bilinear maps with a basis over each argument
 -/

only minor changes required