linear_algebra.matrix.to_linear_equiv ⟷ Mathlib.LinearAlgebra.Matrix.ToLinearEquiv

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

@@ -123,7 +123,7 @@ section Nondegenerate
 
 open scoped Matrix
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff_aux /-
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
@@ -151,8 +151,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff' /-
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
@@ -193,7 +193,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff /-
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
@@ -201,7 +201,7 @@ theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsD
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_vecMul_eq_zero_iff /-
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by

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

@@ -160,7 +160,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
   by
   have : (∃ (v : _) (_ : v ≠ 0), mul_vec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
     exists_mul_vec_eq_zero_iff_aux
-  rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this 
+  rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this
   refine' Iff.trans _ this; constructor <;> rintro ⟨v, hv, mul_eq⟩
   · refine' ⟨fun i => algebraMap _ _ (v i), mt (fun h => funext fun i => _) hv, _⟩
     · exact is_fraction_ring.to_map_eq_zero_iff.mp (congr_fun h i)
@@ -176,7 +176,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
         mt (fun h => funext fun i => _) hv, _⟩
     · have := congr_arg (algebraMap A K) (congr_fun h i)
       rw [hf, Subtype.coe_mk, Pi.zero_apply, RingHom.map_zero, Algebra.smul_def, mul_eq_zero,
-        IsFractionRing.to_map_eq_zero_iff] at this 
+        IsFractionRing.to_map_eq_zero_iff] at this
       exact this.resolve_left (nonZeroDivisors.ne_zero hb)
     · ext i
       refine' IsFractionRing.injective A K _

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

@@ -3,13 +3,13 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 -/
-import Mathbin.LinearAlgebra.FiniteDimensional
-import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
-import Mathbin.LinearAlgebra.Matrix.Nondegenerate
-import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
-import Mathbin.LinearAlgebra.Matrix.ToLin
-import Mathbin.RingTheory.Localization.FractionRing
-import Mathbin.RingTheory.Localization.Integer
+import LinearAlgebra.FiniteDimensional
+import LinearAlgebra.Matrix.GeneralLinearGroup
+import LinearAlgebra.Matrix.Nondegenerate
+import LinearAlgebra.Matrix.NonsingularInverse
+import LinearAlgebra.Matrix.ToLin
+import RingTheory.Localization.FractionRing
+import RingTheory.Localization.Integer
 
 #align_import linear_algebra.matrix.to_linear_equiv from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
 
@@ -123,7 +123,7 @@ section Nondegenerate
 
 open scoped Matrix
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff_aux /-
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
@@ -151,8 +151,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff' /-
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
@@ -193,7 +193,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff /-
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
@@ -201,7 +201,7 @@ theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsD
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_vecMul_eq_zero_iff /-
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -225,7 +225,7 @@ theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A]
 #align matrix.nondegenerate_iff_det_ne_zero Matrix.nondegenerate_iff_det_ne_zero
 -/
 
-alias nondegenerate_iff_det_ne_zero ↔ nondegenerate.det_ne_zero nondegenerate.of_det_ne_zero
+alias ⟨nondegenerate.det_ne_zero, nondegenerate.of_det_ne_zero⟩ := nondegenerate_iff_det_ne_zero
 #align matrix.nondegenerate.det_ne_zero Matrix.Nondegenerate.det_ne_zero
 #align matrix.nondegenerate.of_det_ne_zero Matrix.Nondegenerate.of_det_ne_zero
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.to_linear_equiv
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.FiniteDimensional
 import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
@@ -16,6 +11,8 @@ import Mathbin.LinearAlgebra.Matrix.ToLin
 import Mathbin.RingTheory.Localization.FractionRing
 import Mathbin.RingTheory.Localization.Integer
 
+#align_import linear_algebra.matrix.to_linear_equiv from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 # Matrices and linear equivalences
 
@@ -126,7 +123,7 @@ section Nondegenerate
 
 open scoped Matrix
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff_aux /-
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
@@ -154,8 +151,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff' /-
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
@@ -196,7 +193,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_mulVec_eq_zero_iff /-
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
@@ -204,7 +201,7 @@ theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsD
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 #print Matrix.exists_vecMul_eq_zero_iff /-
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by

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

@@ -52,6 +52,7 @@ section ToLinearEquiv'
 
 variable [DecidableEq n]
 
+#print Matrix.toLinearEquiv' /-
 /-- An invertible matrix yields a linear equivalence from the free module to itself.
 
 See `matrix.to_linear_equiv` for the same map on arbitrary modules.
@@ -60,18 +61,23 @@ def toLinearEquiv' (P : Matrix n n R) (h : Invertible P) : (n → R) ≃ₗ[R] n
   GeneralLinearGroup.generalLinearEquiv _ _ <|
     Matrix.GeneralLinearGroup.toLinear <| unitOfInvertible P
 #align matrix.to_linear_equiv' Matrix.toLinearEquiv'
+-/
 
+#print Matrix.toLinearEquiv'_apply /-
 @[simp]
 theorem toLinearEquiv'_apply (P : Matrix n n R) (h : Invertible P) :
     (↑(P.toLinearEquiv' h) : Module.End R (n → R)) = P.toLin' :=
   rfl
 #align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_apply
+-/
 
+#print Matrix.toLinearEquiv'_symm_apply /-
 @[simp]
 theorem toLinearEquiv'_symm_apply (P : Matrix n n R) (h : Invertible P) :
     (↑(P.toLinearEquiv' h).symm : Module.End R (n → R)) = (⅟ P).toLin' :=
   rfl
 #align matrix.to_linear_equiv'_symm_apply Matrix.toLinearEquiv'_symm_apply
+-/
 
 end ToLinearEquiv'
 
@@ -79,8 +85,7 @@ section ToLinearEquiv
 
 variable (b : Basis n R M)
 
-include b
-
+#print Matrix.toLinearEquiv /-
 /-- Given `hA : is_unit A.det` and `b : basis R b`, `A.to_linear_equiv b hA` is
 the `linear_equiv` arising from `to_lin b b A`.
 
@@ -99,16 +104,21 @@ noncomputable def toLinearEquiv [DecidableEq n] (A : Matrix n n R) (hA : IsUnit
     simp only [← Matrix.toLin_mul b b b, Matrix.nonsing_inv_mul _ hA, Matrix.mul_nonsing_inv _ hA,
       to_lin_one, LinearMap.id_apply]
 #align matrix.to_linear_equiv Matrix.toLinearEquiv
+-/
 
+#print Matrix.ker_toLin_eq_bot /-
 theorem ker_toLin_eq_bot [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).ker = ⊥ :=
   ker_eq_bot.mpr (toLinearEquiv b A hA).Injective
 #align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_bot
+-/
 
+#print Matrix.range_toLin_eq_top /-
 theorem range_toLin_eq_top [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).range = ⊤ :=
   range_eq_top.mpr (toLinearEquiv b A hA).Surjective
 #align matrix.range_to_lin_eq_top Matrix.range_toLin_eq_top
+-/
 
 end ToLinearEquiv
 
@@ -117,6 +127,7 @@ section Nondegenerate
 open scoped Matrix
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+#print Matrix.exists_mulVec_eq_zero_iff_aux /-
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M : Matrix n n K} :
@@ -141,9 +152,11 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
       exact (LinearEquiv.ofInjectiveEndo M.to_lin' this).apply_symm_apply v
     exact Matrix.det_ne_zero_of_right_inverse this
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+#print Matrix.exists_mulVec_eq_zero_iff' /-
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
     (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
@@ -181,19 +194,25 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
           RingHom.mapMatrix_apply, Pi.smul_apply, smul_eq_mul, Algebra.smul_def]
       · rw [mul_vec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+#print Matrix.exists_mulVec_eq_zero_iff /-
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+#print Matrix.exists_vecMul_eq_zero_iff /-
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mul_vec_transpose] using exists_mul_vec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
+-/
 
+#print Matrix.nondegenerate_iff_det_ne_zero /-
 theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : Nondegenerate M ↔ M.det ≠ 0 :=
   by
@@ -207,6 +226,7 @@ theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A]
     refine' not_imp_not.mp (h v) (funext fun i => _)
     simpa only [dot_product_mul_vec, dot_product_single, mul_one] using hv (Pi.single i 1)
 #align matrix.nondegenerate_iff_det_ne_zero Matrix.nondegenerate_iff_det_ne_zero
+-/
 
 alias nondegenerate_iff_det_ne_zero ↔ nondegenerate.det_ne_zero nondegenerate.of_det_ne_zero
 #align matrix.nondegenerate.det_ne_zero Matrix.Nondegenerate.det_ne_zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -176,7 +176,6 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
           _
         _ = 0 := _
         _ = algebraMap A K 0 := (RingHom.map_zero _).symm
-        
       ·
         simp_rw [RingHom.map_mulVec, mul_vec, dot_product, Function.comp_apply, hf, Subtype.coe_mk,
           RingHom.mapMatrix_apply, Pi.smul_apply, smul_eq_mul, Algebra.smul_def]

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -116,7 +116,7 @@ section Nondegenerate
 
 open scoped Matrix
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M : Matrix n n K} :
@@ -142,8 +142,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
     exact Matrix.det_ne_zero_of_right_inverse this
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
     (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
@@ -183,13 +183,13 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
       · rw [mul_vec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mul_vec_transpose] using exists_mul_vec_eq_zero_iff

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

@@ -120,7 +120,7 @@ open scoped Matrix
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M : Matrix n n K} :
-    (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
+    (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   by
   constructor
   · rintro ⟨v, hv, mul_eq⟩
@@ -146,11 +146,11 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
-    (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
+    (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   by
-  have : (∃ (v : _)(_ : v ≠ 0), mul_vec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
+  have : (∃ (v : _) (_ : v ≠ 0), mul_vec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
     exists_mul_vec_eq_zero_iff_aux
-  rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this
+  rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this 
   refine' Iff.trans _ this; constructor <;> rintro ⟨v, hv, mul_eq⟩
   · refine' ⟨fun i => algebraMap _ _ (v i), mt (fun h => funext fun i => _) hv, _⟩
     · exact is_fraction_ring.to_map_eq_zero_iff.mp (congr_fun h i)
@@ -166,7 +166,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
         mt (fun h => funext fun i => _) hv, _⟩
     · have := congr_arg (algebraMap A K) (congr_fun h i)
       rw [hf, Subtype.coe_mk, Pi.zero_apply, RingHom.map_zero, Algebra.smul_def, mul_eq_zero,
-        IsFractionRing.to_map_eq_zero_iff] at this
+        IsFractionRing.to_map_eq_zero_iff] at this 
       exact this.resolve_left (nonZeroDivisors.ne_zero hb)
     · ext i
       refine' IsFractionRing.injective A K _
@@ -185,13 +185,13 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
+    {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
+    {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mul_vec_transpose] using exists_mul_vec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
 

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

@@ -114,7 +114,7 @@ end ToLinearEquiv
 
 section Nondegenerate
 
-open Matrix
+open scoped Matrix
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),

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

@@ -52,12 +52,6 @@ section ToLinearEquiv'
 
 variable [DecidableEq n]
 
-/- warning: matrix.to_linear_equiv' -> Matrix.toLinearEquiv' is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv' Matrix.toLinearEquiv'ₓ'. -/
 /-- An invertible matrix yields a linear equivalence from the free module to itself.
 
 See `matrix.to_linear_equiv` for the same map on arbitrary modules.
@@ -67,18 +61,12 @@ def toLinearEquiv' (P : Matrix n n R) (h : Invertible P) : (n → R) ≃ₗ[R] n
     Matrix.GeneralLinearGroup.toLinear <| unitOfInvertible P
 #align matrix.to_linear_equiv' Matrix.toLinearEquiv'
 
-/- warning: matrix.to_linear_equiv'_apply -> Matrix.toLinearEquiv'_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_applyₓ'. -/
 @[simp]
 theorem toLinearEquiv'_apply (P : Matrix n n R) (h : Invertible P) :
     (↑(P.toLinearEquiv' h) : Module.End R (n → R)) = P.toLin' :=
   rfl
 #align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_apply
 
-/- warning: matrix.to_linear_equiv'_symm_apply -> Matrix.toLinearEquiv'_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv'_symm_apply Matrix.toLinearEquiv'_symm_applyₓ'. -/
 @[simp]
 theorem toLinearEquiv'_symm_apply (P : Matrix n n R) (h : Invertible P) :
     (↑(P.toLinearEquiv' h).symm : Module.End R (n → R)) = (⅟ P).toLin' :=
@@ -93,12 +81,6 @@ variable (b : Basis n R M)
 
 include b
 
-/- warning: matrix.to_linear_equiv -> Matrix.toLinearEquiv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv Matrix.toLinearEquivₓ'. -/
 /-- Given `hA : is_unit A.det` and `b : basis R b`, `A.to_linear_equiv b hA` is
 the `linear_equiv` arising from `to_lin b b A`.
 
@@ -118,17 +100,11 @@ noncomputable def toLinearEquiv [DecidableEq n] (A : Matrix n n R) (hA : IsUnit
       to_lin_one, LinearMap.id_apply]
 #align matrix.to_linear_equiv Matrix.toLinearEquiv
 
-/- warning: matrix.ker_to_lin_eq_bot -> Matrix.ker_toLin_eq_bot is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_botₓ'. -/
 theorem ker_toLin_eq_bot [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).ker = ⊥ :=
   ker_eq_bot.mpr (toLinearEquiv b A hA).Injective
 #align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_bot
 
-/- warning: matrix.range_to_lin_eq_top -> Matrix.range_toLin_eq_top is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.range_to_lin_eq_top Matrix.range_toLin_eq_topₓ'. -/
 theorem range_toLin_eq_top [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).range = ⊤ :=
   range_eq_top.mpr (toLinearEquiv b A hA).Surjective
@@ -140,12 +116,6 @@ section Nondegenerate
 
 open Matrix
 
-/- warning: matrix.exists_mul_vec_eq_zero_iff_aux -> Matrix.exists_mulVec_eq_zero_iff_aux is a dubious translation:
-lean 3 declaration is
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
@@ -172,12 +142,6 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
     exact Matrix.det_ne_zero_of_right_inverse this
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 
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-Case conversion may be inaccurate. Consider using '#align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
@@ -219,36 +183,18 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
       · rw [mul_vec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mul_vec_transpose] using exists_mul_vec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
 
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 theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : Nondegenerate M ↔ M.det ≠ 0 :=
   by
@@ -263,18 +209,6 @@ theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A]
     simpa only [dot_product_mul_vec, dot_product_single, mul_one] using hv (Pi.single i 1)
 #align matrix.nondegenerate_iff_det_ne_zero Matrix.nondegenerate_iff_det_ne_zero
 
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 alias nondegenerate_iff_det_ne_zero ↔ nondegenerate.det_ne_zero nondegenerate.of_det_ne_zero
 #align matrix.nondegenerate.det_ne_zero Matrix.Nondegenerate.det_ne_zero
 #align matrix.nondegenerate.of_det_ne_zero Matrix.Nondegenerate.of_det_ne_zero

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

@@ -68,10 +68,7 @@ def toLinearEquiv' (P : Matrix n n R) (h : Invertible P) : (n → R) ≃ₗ[R] n
 #align matrix.to_linear_equiv' Matrix.toLinearEquiv'
 
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin'._proof_2.{u1} R (CommRing.toCommSemiring.{u1} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i 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u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n R) => LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R 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_inst_1)))))))) (Matrix.toLin'.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n n _inst_4 (fun (a : n) (b : n) => _inst_5 a b)) P)
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_applyₓ'. -/
 @[simp]
 theorem toLinearEquiv'_apply (P : Matrix n n R) (h : Invertible P) :
@@ -80,10 +77,7 @@ theorem toLinearEquiv'_apply (P : Matrix n n R) (h : Invertible P) :
 #align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_apply
 
 /- warning: matrix.to_linear_equiv'_symm_apply -> Matrix.toLinearEquiv'_symm_apply is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (Matrix.{u2, u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n R) => LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R 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(a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun 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(CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun 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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv'_symm_apply Matrix.toLinearEquiv'_symm_applyₓ'. -/
 @[simp]
 theorem toLinearEquiv'_symm_apply (P : Matrix n n R) (h : Invertible P) :
@@ -125,10 +119,7 @@ noncomputable def toLinearEquiv [DecidableEq n] (A : Matrix n n R) (hA : IsUnit
 #align matrix.to_linear_equiv Matrix.toLinearEquiv
 
 /- warning: matrix.ker_to_lin_eq_bot -> Matrix.ker_toLin_eq_bot is a dubious translation:
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(RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (SMulZeroClass.toSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (AddMonoid.toZero.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (AddMonoid.toAddZeroClass.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u2, max u2 u3, u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u3, u1, max (max u2 u1) u3} R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u3, u1, max (max u2 u1) u3} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_botₓ'. -/
 theorem ker_toLin_eq_bot [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).ker = ⊥ :=
@@ -136,10 +127,7 @@ theorem ker_toLin_eq_bot [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det)
 #align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_bot
 
 /- warning: matrix.range_to_lin_eq_top -> Matrix.range_toLin_eq_top is a dubious translation:
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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) 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(Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u2, max u2 u3, u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u3, u1, max (max u2 u1) u3} R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u3, u1, max (max u2 u1) u3} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u3, u1} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Matrix.toLin.{u2, u3, u3, u1, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) n n _inst_4 _inst_4 (fun (a : n) (b : n) => _inst_5 a b) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 b b) A)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.range_to_lin_eq_top Matrix.range_toLin_eq_topₓ'. -/
 theorem range_toLin_eq_top [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).range = ⊤ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.to_linear_equiv
-! leanprover-community/mathlib commit e42cfdb03b7902f8787a1eb552cb8f77766b45b9
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.RingTheory.Localization.Integer
 /-!
 # Matrices and linear equivalences
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file gives the map `matrix.to_linear_equiv` from matrices with invertible determinant,
 to linear equivs.
 

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

@@ -49,6 +49,12 @@ section ToLinearEquiv'
 
 variable [DecidableEq n]
 
+/- warning: matrix.to_linear_equiv' -> Matrix.toLinearEquiv' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_4 : Fintype.{u2} n] [_inst_5 : DecidableEq.{succ u2} n] (P : Matrix.{u2, u2, u1} n n R), (Invertible.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) P) -> (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Matrix.toLinearEquiv'._proof_1.{u1} R _inst_1) (Matrix.toLinearEquiv'._proof_2.{u1} R _inst_1) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.Function.module.{u2, u1, u1} n R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_4 : Fintype.{u2} n] [_inst_5 : DecidableEq.{succ u2} n] (P : Matrix.{u2, u2, u1} n n R), (Invertible.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.instMulMatrix.{u1, u2} n R _inst_4 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.one.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) P) -> (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv._hyg.100 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv._hyg.100 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv' Matrix.toLinearEquiv'ₓ'. -/
 /-- An invertible matrix yields a linear equivalence from the free module to itself.
 
 See `matrix.to_linear_equiv` for the same map on arbitrary modules.
@@ -58,12 +64,24 @@ def toLinearEquiv' (P : Matrix n n R) (h : Invertible P) : (n → R) ≃ₗ[R] n
     Matrix.GeneralLinearGroup.toLinear <| unitOfInvertible P
 #align matrix.to_linear_equiv' Matrix.toLinearEquiv'
 
+/- warning: matrix.to_linear_equiv'_apply -> Matrix.toLinearEquiv'_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_4 : Fintype.{u2} n] [_inst_5 : DecidableEq.{succ u2} n] (P : Matrix.{u2, u2, u1} n n R) (h : Invertible.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin'._proof_2.{u1} R (CommRing.toCommSemiring.{u1} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n))) => (Matrix.{u2, u2, u1} n n R) -> (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u2 u1, max u2 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u2 u1, max u2 u1} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, max u2 u1, max u2 u1} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin'._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.toLin'.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n n _inst_4 (fun (a : n) (b : n) => _inst_5 a b)) P)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_4 : Fintype.{u2} n] [_inst_5 : DecidableEq.{succ u2} n] (P : Matrix.{u2, u2, u1} n n R) (h : Invertible.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.instMulMatrix.{u1, u2} n R _inst_4 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.one.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) P), Eq.{max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R 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(fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv._hyg.100 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (ᾰ : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv._hyg.100 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.toLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv._hyg.100 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (Matrix.{u2, u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n R) => LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SemilinearMapClass.distribMulActionHomClass.{u1, max u2 u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1)))))))) (Matrix.toLin'.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n n _inst_4 (fun (a : n) (b : n) => _inst_5 a b)) P)
+Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_applyₓ'. -/
 @[simp]
 theorem toLinearEquiv'_apply (P : Matrix n n R) (h : Invertible P) :
     (↑(P.toLinearEquiv' h) : Module.End R (n → R)) = P.toLin' :=
   rfl
 #align matrix.to_linear_equiv'_apply Matrix.toLinearEquiv'_apply
 
+/- warning: matrix.to_linear_equiv'_symm_apply -> Matrix.toLinearEquiv'_symm_apply is a dubious translation:
+lean 3 declaration is
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, max u2 u1, max u2 u1} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.Function.module.{u2, u1, u1} n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin'._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin'._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.toLin'.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n n _inst_4 (fun (a : n) (b : n) => _inst_5 a b)) (Invertible.invOf.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) P h))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_4 : Fintype.{u2} n] [_inst_5 : DecidableEq.{succ u2} n] (P : Matrix.{u2, u2, u1} n n R) (h : Invertible.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.instMulMatrix.{u1, u2} n R _inst_4 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.one.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) P), Eq.{max (succ u1) (succ u2)} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R 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(CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.toLinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv._hyg.100 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (Matrix.{u2, u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n R) => LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toZero.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (AddMonoid.toAddZeroClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toZero.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, max u2 u1, max u2 u1} (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, max u2 u1} R (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, max u2 u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearEquiv.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R 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_inst_1))))) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun 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(CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R (Matrix.{u2, u2, u1} n n R) (LinearMap.{u1, u1, max u1 u2, max u1 u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (n -> R) (n -> R) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u2, u2} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, max u1 u2, max u1 u2} R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u2, u2, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, max u1 u2, max u1 u2} R R R (n -> R) (n -> R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.addCommMonoid.{u2, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2099 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Pi.module.{u2, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (i : n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (i : n) => Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Pi.smulCommClass.{u2, u1, u1, u1} n (fun (a._@.Mathlib.LinearAlgebra.Matrix.ToLin._hyg.2102 : n) => R) R R (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => Algebra.toSMul.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (i : n) => smulCommClass_self.{u1, u1} R R (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u1} R R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Matrix.toLin'.{u1, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n n _inst_4 (fun (a : n) (b : n) => _inst_5 a b)) (Invertible.invOf.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.instMulMatrix.{u1, u2} n R _inst_4 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Matrix.one.{u1, u2} n R (fun (a : n) (b : n) => _inst_5 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) P h))
+Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv'_symm_apply Matrix.toLinearEquiv'_symm_applyₓ'. -/
 @[simp]
 theorem toLinearEquiv'_symm_apply (P : Matrix n n R) (h : Invertible P) :
     (↑(P.toLinearEquiv' h).symm : Module.End R (n → R)) = (⅟ P).toLin' :=
@@ -78,6 +96,12 @@ variable (b : Basis n R M)
 
 include b
 
+/- warning: matrix.to_linear_equiv -> Matrix.toLinearEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n], (Basis.{u3, u1, u2} n R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (forall [_inst_5 : DecidableEq.{succ u3} n] (A : Matrix.{u3, u3, u1} n n R), (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) -> (LinearEquiv.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Matrix.toLinearEquiv._proof_1.{u1} R _inst_1) (Matrix.toLinearEquiv._proof_2.{u1} R _inst_1) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n], (Basis.{u3, u1, u2} n R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) -> (forall [_inst_5 : DecidableEq.{succ u3} n] (A : Matrix.{u3, u3, u1} n n R), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) -> (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3))
+Case conversion may be inaccurate. Consider using '#align matrix.to_linear_equiv Matrix.toLinearEquivₓ'. -/
 /-- Given `hA : is_unit A.det` and `b : basis R b`, `A.to_linear_equiv b hA` is
 the `linear_equiv` arising from `to_lin b b A`.
 
@@ -97,11 +121,23 @@ noncomputable def toLinearEquiv [DecidableEq n] (A : Matrix n n R) (hA : IsUnit
       to_lin_one, LinearMap.id_apply]
 #align matrix.to_linear_equiv Matrix.toLinearEquiv
 
+/- warning: matrix.ker_to_lin_eq_bot -> Matrix.ker_toLin_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] (b : Basis.{u3, u1, u2} n R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : DecidableEq.{succ u3} n] (A : Matrix.{u3, u3, u1} n n R), (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] (b : Basis.{u3, u2, u1} n R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_5 : DecidableEq.{succ u3} n] (A : Matrix.{u3, u3, u2} n n R), (IsUnit.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.ker.{u2, u2, u1, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u3, u3, u2} n n R) => LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) A) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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_inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (Matrix.{u3, u3, u2} n n R) (fun (_x : Matrix.{u3, u3, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u3, u3, u2} n n R) => LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u3, u2, max u2 u3, u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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_inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (SMulZeroClass.toSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (AddMonoid.toZero.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (AddMonoid.toAddZeroClass.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u2, max u2 u3, u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u3, u1, max (max u2 u1) u3} R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) 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(CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u3, u1, max (max u2 u1) u3} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) 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(Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u3, u1} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Matrix.toLin.{u2, u3, u3, u1, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) n n _inst_4 _inst_4 (fun (a : n) (b : n) => _inst_5 a b) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 b b) A)) (Bot.bot.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instBotSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_botₓ'. -/
 theorem ker_toLin_eq_bot [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).ker = ⊥ :=
   ker_eq_bot.mpr (toLinearEquiv b A hA).Injective
 #align matrix.ker_to_lin_eq_bot Matrix.ker_toLin_eq_bot
 
+/- warning: matrix.range_to_lin_eq_top -> Matrix.range_toLin_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] (b : Basis.{u3, u1, u2} n R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) [_inst_5 : DecidableEq.{succ u3} n] (A : Matrix.{u3, u3, u1} n n R), (IsUnit.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{max (succ (max u3 u1)) (succ u2), max (succ (max u3 u1)) (succ u2)} (LinearEquiv.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.{u3, u3, u1} n n R) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u1, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u3, u3, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (Matrix.toLin._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) (fun (_x : LinearEquiv.{u1, u1, max u3 u1, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.{u3, u3, u1} n n R) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u1, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u3, u3, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (Matrix.toLin._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3))) => (Matrix.{u3, u3, u1} n n R) -> (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3)) (LinearEquiv.hasCoeToFun.{u1, u1, max u3 u1, u2} R R (Matrix.{u3, u3, u1} n n R) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.module.{u1, u3, u3, u1} n n R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (Matrix.toLin._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.toLin._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.toLin._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.toLin.{u1, u3, u3, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) n n _inst_4 _inst_4 (fun (a : n) (b : n) => _inst_5 a b) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3 _inst_3 b b) A)) (Top.top.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3)))
+but is expected to have type
+  forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : AddCommGroup.{u1} M] [_inst_3 : Module.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2)] {n : Type.{u3}} [_inst_4 : Fintype.{u3} n] (b : Basis.{u3, u2, u1} n R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) [_inst_5 : DecidableEq.{succ u3} n] (A : Matrix.{u3, u3, u2} n n R), (IsUnit.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 R _inst_1 A)) -> (Eq.{succ u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (LinearMap.range.{u2, u2, u1, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u3, u3, u2} n n R) => LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) A) (LinearMap.semilinearMapClass.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), succ u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toZero.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddMonoid.toAddZeroClass.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u3, u2, max u2 u3, u1} (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u2 u3} (Matrix.{u3, u3, u2} n n R) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, max u2 u3} R (Matrix.{u3, u3, u2} n n R) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 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(AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u3, u1, max (max u2 u1) u3} R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u3, u1, max (max u2 u1) u3} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (LinearEquiv.{u2, u2, max u2 u3, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u3, u1} R R (Matrix.{u3, u3, u2} n n R) (LinearMap.{u2, u2, u1, u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Matrix.addCommMonoid.{u2, u3, u3} n n R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (LinearMap.addCommMonoid.{u2, u2, u1, u1} R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Matrix.module.{u2, u3, u3, u2} n n R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u1} R R R M M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) _inst_3 (smulCommClass_self.{u2, u1} R M (CommSemiring.toCommMonoid.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (MulActionWithZero.toMulAction.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (Matrix.toLin.{u2, u3, u3, u1, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) n n _inst_4 _inst_4 (fun (a : n) (b : n) => _inst_5 a b) M M (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3 _inst_3 b b) A)) (Top.top.{u1} (Submodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3) (Submodule.instTopSubmodule.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align matrix.range_to_lin_eq_top Matrix.range_toLin_eq_topₓ'. -/
 theorem range_toLin_eq_top [DecidableEq n] (A : Matrix n n R) (hA : IsUnit A.det) :
     (toLin b b A).range = ⊤ :=
   range_eq_top.mpr (toLinearEquiv b A hA).Surjective
@@ -113,6 +149,12 @@ section Nondegenerate
 
 open Matrix
 
+/- warning: matrix.exists_mul_vec_eq_zero_iff_aux -> Matrix.exists_mulVec_eq_zero_iff_aux is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {K : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : Field.{u2} K] {M : Matrix.{u1, u1, u2} n n K}, Iff (Exists.{succ (max u1 u2)} (n -> K) (fun (v : n -> K) => Exists.{0} (Ne.{succ (max u1 u2)} (n -> K) v (OfNat.ofNat.{max u1 u2} (n -> K) 0 (OfNat.mk.{max u1 u2} (n -> K) 0 (Zero.zero.{max u1 u2} (n -> K) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => K) (fun (i : n) => MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_6)))))))))))) (fun (H : Ne.{succ (max u1 u2)} (n -> K) v (OfNat.ofNat.{max u1 u2} (n -> K) 0 (OfNat.mk.{max u1 u2} (n -> K) 0 (Zero.zero.{max u1 u2} (n -> K) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => K) (fun (i : n) => MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_6)))))))))))) => Eq.{max (succ u1) (succ u2)} (n -> K) (Matrix.mulVec.{u2, u1, u1} n n K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_6))))) _inst_4 M v) (OfNat.ofNat.{max u1 u2} (n -> K) 0 (OfNat.mk.{max u1 u2} (n -> K) 0 (Zero.zero.{max u1 u2} (n -> K) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => K) (fun (i : n) => MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_6)))))))))))))) (Eq.{succ u2} K (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_6)) M) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_6)))))))))))
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {K : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : Field.{u2} K] {M : Matrix.{u1, u1, u2} n n K}, Iff (Exists.{succ (max u1 u2)} (n -> K) (fun (v : n -> K) => Exists.{0} (Ne.{succ (max u1 u2)} (n -> K) v (OfNat.ofNat.{max u1 u2} (n -> K) 0 (Zero.toOfNat0.{max u1 u2} (n -> K) (Pi.instZero.{u1, u2} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => K) (fun (i : n) => CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_6)))))))) (fun (H : Ne.{succ (max u1 u2)} (n -> K) v (OfNat.ofNat.{max u1 u2} (n -> K) 0 (Zero.toOfNat0.{max u1 u2} (n -> K) (Pi.instZero.{u1, u2} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => K) (fun (i : n) => CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_6)))))))) => Eq.{max (succ u1) (succ u2)} (n -> K) (Matrix.mulVec.{u2, u1, u1} n n K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_6))))) _inst_4 M v) (OfNat.ofNat.{max u1 u2} (n -> K) 0 (Zero.toOfNat0.{max u1 u2} (n -> K) (Pi.instZero.{u1, u2} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => K) (fun (i : n) => CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_6)))))))))) (Eq.{succ u2} K (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_6)) M) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_6)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_auxₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
@@ -139,6 +181,12 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
     exact Matrix.det_ne_zero_of_right_inverse this
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 
+/- warning: matrix.exists_mul_vec_eq_zero_iff' -> Matrix.exists_mulVec_eq_zero_iff' is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u2}} (K : Type.{u3}) [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u2} A] [_inst_7 : Nontrivial.{u2} A] [_inst_8 : Field.{u3} K] [_inst_9 : Algebra.{u2, u3} A K (CommRing.toCommSemiring.{u2} A _inst_6) (Ring.toSemiring.{u3} K (DivisionRing.toRing.{u3} K (Field.toDivisionRing.{u3} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u3} A _inst_6 K (EuclideanDomain.toCommRing.{u3} K (Field.toEuclideanDomain.{u3} K _inst_8)) _inst_9] {M : Matrix.{u1, u1, u2} n n A}, Iff (Exists.{succ (max u1 u2)} (n -> A) (fun (v : n -> A) => Exists.{0} (Ne.{succ (max u1 u2)} (n -> A) v (OfNat.ofNat.{max u1 u2} (n -> A) 0 (OfNat.mk.{max u1 u2} (n -> A) 0 (Zero.zero.{max u1 u2} (n -> A) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => A) (fun (i : n) => MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))) (fun (H : Ne.{succ (max u1 u2)} (n -> A) v (OfNat.ofNat.{max u1 u2} (n -> A) 0 (OfNat.mk.{max u1 u2} (n -> A) 0 (Zero.zero.{max u1 u2} (n -> A) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => A) (fun (i : n) => MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))) => Eq.{max (succ u1) (succ u2)} (n -> A) (Matrix.mulVec.{u2, u1, u1} n n A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6)))) _inst_4 M v) (OfNat.ofNat.{max u1 u2} (n -> A) 0 (OfNat.mk.{max u1 u2} (n -> A) 0 (Zero.zero.{max u1 u2} (n -> A) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => A) (fun (i : n) => MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))))) (Eq.{succ u2} A (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u3}} (K : Type.{u2}) [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u3} A] [_inst_7 : Nontrivial.{u3} A] [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u3, u2} A K (CommRing.toCommSemiring.{u3} A _inst_6) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u3, u2} A _inst_6 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_8)) _inst_9] {M : Matrix.{u1, u1, u3} n n A}, Iff (Exists.{succ (max u1 u3)} (n -> A) (fun (v : n -> A) => Exists.{0} (Ne.{succ (max u1 u3)} (n -> A) v (OfNat.ofNat.{max u1 u3} (n -> A) 0 (Zero.toOfNat0.{max u1 u3} (n -> A) (Pi.instZero.{u1, u3} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => A) (fun (i : n) => CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A (CommRing.toCommSemiring.{u3} A _inst_6))))))) (fun (H : Ne.{succ (max u1 u3)} (n -> A) v (OfNat.ofNat.{max u1 u3} (n -> A) 0 (Zero.toOfNat0.{max u1 u3} (n -> A) (Pi.instZero.{u1, u3} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => A) (fun (i : n) => CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A (CommRing.toCommSemiring.{u3} A _inst_6))))))) => Eq.{max (succ u1) (succ u3)} (n -> A) (Matrix.mulVec.{u3, u1, u1} n n A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_6)))) _inst_4 M v) (OfNat.ofNat.{max u1 u3} (n -> A) 0 (Zero.toOfNat0.{max u1 u3} (n -> A) (Pi.instZero.{u1, u3} n (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.18074 : n) => A) (fun (i : n) => CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A (CommRing.toCommSemiring.{u3} A _inst_6))))))))) (Eq.{succ u3} A (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u3} A 0 (Zero.toOfNat0.{u3} A (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A (CommRing.toCommSemiring.{u3} A _inst_6))))))
+Case conversion may be inaccurate. Consider using '#align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
@@ -180,18 +228,36 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
       · rw [mul_vec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
+/- warning: matrix.exists_mul_vec_eq_zero_iff -> Matrix.exists_mulVec_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u2} A] [_inst_7 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_6))] {M : Matrix.{u1, u1, u2} n n A}, Iff (Exists.{succ (max u1 u2)} (n -> A) (fun (v : n -> A) => Exists.{0} (Ne.{succ (max u1 u2)} (n -> A) v (OfNat.ofNat.{max u1 u2} (n -> A) 0 (OfNat.mk.{max u1 u2} (n -> A) 0 (Zero.zero.{max u1 u2} (n -> A) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => A) (fun (i : n) => MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))) (fun (H : Ne.{succ (max u1 u2)} (n -> A) v (OfNat.ofNat.{max u1 u2} (n -> A) 0 (OfNat.mk.{max u1 u2} (n -> A) 0 (Zero.zero.{max u1 u2} (n -> A) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => A) (fun (i : n) => MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))) => Eq.{max (succ u1) (succ u2)} (n -> A) (Matrix.mulVec.{u2, u1, u1} n n A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6)))) _inst_4 M v) (OfNat.ofNat.{max u1 u2} (n -> A) 0 (OfNat.mk.{max u1 u2} (n -> A) 0 (Zero.zero.{max u1 u2} (n -> A) (Pi.instZero.{u1, u2} n (fun (ᾰ : n) => A) (fun (i : n) => MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))))) (Eq.{succ u2} A (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))
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+Case conversion may be inaccurate. Consider using '#align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
+/- warning: matrix.exists_vec_mul_eq_zero_iff -> Matrix.exists_vecMul_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mul_vec_transpose] using exists_mul_vec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
 
+/- warning: matrix.nondegenerate_iff_det_ne_zero -> Matrix.nondegenerate_iff_det_ne_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.nondegenerate_iff_det_ne_zero Matrix.nondegenerate_iff_det_ne_zeroₓ'. -/
 theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : Nondegenerate M ↔ M.det ≠ 0 :=
   by
@@ -206,6 +272,18 @@ theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A]
     simpa only [dot_product_mul_vec, dot_product_single, mul_one] using hv (Pi.single i 1)
 #align matrix.nondegenerate_iff_det_ne_zero Matrix.nondegenerate_iff_det_ne_zero
 
+/- warning: matrix.nondegenerate.det_ne_zero -> Matrix.Nondegenerate.det_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u2} A] [_inst_7 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_6))] {M : Matrix.{u1, u1, u2} n n A}, (Matrix.Nondegenerate.{u1, u2} n A _inst_4 _inst_6 M) -> (Ne.{succ u2} A (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6))))))))))
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u2} A] [_inst_7 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_6))] {M : Matrix.{u1, u1, u2} n n A}, (Matrix.Nondegenerate.{u1, u2} n A _inst_4 _inst_6 M) -> (Ne.{succ u2} A (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_6) _inst_7))))))
+Case conversion may be inaccurate. Consider using '#align matrix.nondegenerate.det_ne_zero Matrix.Nondegenerate.det_ne_zeroₓ'. -/
+/- warning: matrix.nondegenerate.of_det_ne_zero -> Matrix.Nondegenerate.of_det_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u2} A] [_inst_7 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_6))] {M : Matrix.{u1, u1, u2} n n A}, (Ne.{succ u2} A (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_6)))))))))) -> (Matrix.Nondegenerate.{u1, u2} n A _inst_4 _inst_6 M)
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_4 : Fintype.{u1} n] {A : Type.{u2}} [_inst_5 : DecidableEq.{succ u1} n] [_inst_6 : CommRing.{u2} A] [_inst_7 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_6))] {M : Matrix.{u1, u1, u2} n n A}, (Ne.{succ u2} A (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_5 a b) _inst_4 A _inst_6 M) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_6) _inst_7)))))) -> (Matrix.Nondegenerate.{u1, u2} n A _inst_4 _inst_6 M)
+Case conversion may be inaccurate. Consider using '#align matrix.nondegenerate.of_det_ne_zero Matrix.Nondegenerate.of_det_ne_zeroₓ'. -/
 alias nondegenerate_iff_det_ne_zero ↔ nondegenerate.det_ne_zero nondegenerate.of_det_ne_zero
 #align matrix.nondegenerate.det_ne_zero Matrix.Nondegenerate.det_ne_zero
 #align matrix.nondegenerate.of_det_ne_zero Matrix.Nondegenerate.of_det_ne_zero

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.to_linear_equiv
-! leanprover-community/mathlib commit b1c23399f01266afe392a0d8f71f599a0dad4f7b
+! leanprover-community/mathlib commit e42cfdb03b7902f8787a1eb552cb8f77766b45b9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.FiniteDimensional
+import Mathbin.LinearAlgebra.Matrix.GeneralLinearGroup
 import Mathbin.LinearAlgebra.Matrix.Nondegenerate
 import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
 import Mathbin.LinearAlgebra.Matrix.ToLin
@@ -53,14 +54,8 @@ variable [DecidableEq n]
 See `matrix.to_linear_equiv` for the same map on arbitrary modules.
 -/
 def toLinearEquiv' (P : Matrix n n R) (h : Invertible P) : (n → R) ≃ₗ[R] n → R :=
-  { P.toLin' with
-    invFun := (⅟ P).toLin'
-    left_inv := fun v =>
-      show ((⅟ P).toLin'.comp P.toLin') v = v by
-        rw [← Matrix.toLin'_mul, P.inv_of_mul_self, Matrix.toLin'_one, LinearMap.id_apply]
-    right_inv := fun v =>
-      show (P.toLin'.comp (⅟ P).toLin') v = v by
-        rw [← Matrix.toLin'_mul, P.mul_inv_of_self, Matrix.toLin'_one, LinearMap.id_apply] }
+  GeneralLinearGroup.generalLinearEquiv _ _ <|
+    Matrix.GeneralLinearGroup.toLinear <| unitOfInvertible P
 #align matrix.to_linear_equiv' Matrix.toLinearEquiv'
 
 @[simp]
@@ -71,8 +66,8 @@ theorem toLinearEquiv'_apply (P : Matrix n n R) (h : Invertible P) :
 
 @[simp]
 theorem toLinearEquiv'_symm_apply (P : Matrix n n R) (h : Invertible P) :
-    (↑(P.toLinearEquiv' h).symm : Module.End R (n → R)) = P⁻¹.toLin' :=
-  show (⅟ P).toLin' = _ from congr_arg _ P.invOf_eq_nonsing_inv
+    (↑(P.toLinearEquiv' h).symm : Module.End R (n → R)) = (⅟ P).toLin' :=
+  rfl
 #align matrix.to_linear_equiv'_symm_apply Matrix.toLinearEquiv'_symm_apply
 
 end ToLinearEquiv'

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.to_linear_equiv
-! leanprover-community/mathlib commit c8ab806ef73c20cab1d87b5157e43a82c205f28e
+! leanprover-community/mathlib commit b1c23399f01266afe392a0d8f71f599a0dad4f7b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.LinearAlgebra.FiniteDimensional
 import Mathbin.LinearAlgebra.Matrix.Nondegenerate
 import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
 import Mathbin.LinearAlgebra.Matrix.ToLin

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

@@ -117,7 +117,7 @@ section Nondegenerate
 
 open Matrix
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 /-- This holds for all integral domains (see `matrix.exists_mul_vec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M : Matrix n n K} :
@@ -143,8 +143,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
     exact Matrix.det_ne_zero_of_right_inverse this
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ≠ » 0) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
     (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
@@ -184,13 +184,13 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
       · rw [mul_vec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (v «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (v «expr ≠ » 0) -/
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mul_vec_transpose] using exists_mul_vec_eq_zero_iff

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

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -221,7 +221,7 @@ lemma det_ne_zero_of_sum_col_pos [DecidableEq n] {S : Type*} [LinearOrderedCommR
         simp_rw [not_exists, not_lt] at h_sup
         refine ⟨i, ?_⟩
         rw [Pi.smul_apply, neg_smul, one_smul, Left.neg_pos_iff]
-        refine Ne.lt_of_le hi (h_sup i)
+        exact Ne.lt_of_le hi (h_sup i)
     · obtain ⟨j₀, -, h_j₀⟩ := Finset.exists_mem_eq_sup' Finset.univ_nonempty v
       refine ⟨j₀, ?_⟩
       rw [← mul_le_mul_left (h_j₀ ▸ h_sup), Finset.mul_sum, mul_zero]

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

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

@@ -113,7 +113,7 @@ open Matrix
 /-- This holds for all integral domains (see `Matrix.exists_mulVec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type*} [DecidableEq n] [Field K] {M : Matrix n n K} :
-    (∃ v ≠ 0, M.mulVec v = 0) ↔ M.det = 0 := by
+    (∃ v ≠ 0, M *ᵥ v = 0) ↔ M.det = 0 := by
   constructor
   · rintro ⟨v, hv, mul_eq⟩
     contrapose! hv
@@ -135,8 +135,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type*} [DecidableEq n] [Field K] {M :
 
 theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
-    (∃ v ≠ 0, M.mulVec v = 0) ↔ M.det = 0 := by
-  have : (∃ v ≠ 0, mulVec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
+    (∃ v ≠ 0, M *ᵥ v = 0) ↔ M.det = 0 := by
+  have : (∃ v ≠ 0, (algebraMap A K).mapMatrix M *ᵥ v = 0) ↔ _ :=
     exists_mulVec_eq_zero_iff_aux
   rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this
   refine' Iff.trans _ this; constructor <;> rintro ⟨v, hv, mul_eq⟩
@@ -159,8 +159,8 @@ theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [Comm
     · ext i
       refine' IsFractionRing.injective A K _
       calc
-        algebraMap A K (M.mulVec (fun i : n => f (v i) _) i) =
-            ((algebraMap A K).mapMatrix M).mulVec (algebraMap _ K b • v) i := ?_
+        algebraMap A K ((M *ᵥ (fun i : n => f (v i) _)) i) =
+            ((algebraMap A K).mapMatrix M *ᵥ algebraMap _ K b • v) i := ?_
         _ = 0 := ?_
         _ = algebraMap A K 0 := (RingHom.map_zero _).symm
       · simp_rw [RingHom.map_mulVec, mulVec, dotProduct, Function.comp_apply, hf,
@@ -169,12 +169,12 @@ theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [Comm
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
 theorem exists_mulVec_eq_zero_iff {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ v ≠ 0, M.mulVec v = 0) ↔ M.det = 0 :=
+    {M : Matrix n n A} : (∃ v ≠ 0, M *ᵥ v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
 theorem exists_vecMul_eq_zero_iff {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ v ≠ 0, M.vecMul v = 0) ↔ M.det = 0 := by
+    {M : Matrix n n A} : (∃ v ≠ 0, v ᵥ* M = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mulVec_transpose] using exists_mulVec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
 

Performed with a regex search for ∀ (.) (.), \1 ≠ \2 →, and a few variants to catch implicit binders and explicit types.

I have deliberately avoided trying to make the analogous Set.Pairwise transformation (or any Pairwise (foo on bar) transformations) in this PR, to keep the diff small.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -206,7 +206,7 @@ open BigOperators
 /-- A matrix whose nondiagonal entries are negative with the sum of the entries of each
 column positive has nonzero determinant. -/
 lemma det_ne_zero_of_sum_col_pos [DecidableEq n] {S : Type*} [LinearOrderedCommRing S]
-    {A : Matrix n n S} (h1 : ∀ i j, i ≠ j → A i j < 0) (h2 : ∀ j, 0 < ∑ i, A i j) :
+    {A : Matrix n n S} (h1 : Pairwise fun i j => A i j < 0) (h2 : ∀ j, 0 < ∑ i, A i j) :
     A.det ≠ 0 := by
   cases isEmpty_or_nonempty n
   · simp
@@ -229,17 +229,17 @@ lemma det_ne_zero_of_sum_col_pos [DecidableEq n] {S : Type*} [LinearOrderedCommR
       refine Finset.sum_le_sum (fun i hi => ?_)
       by_cases h : i = j₀
       · rw [h]
-      · exact (mul_le_mul_right_of_neg (h1 i j₀ h)).mpr (h_j₀ ▸ Finset.le_sup' v hi)
+      · exact (mul_le_mul_right_of_neg (h1 h)).mpr (h_j₀ ▸ Finset.le_sup' v hi)
 
 /-- A matrix whose nondiagonal entries are negative with the sum of the entries of each
 row positive has nonzero determinant. -/
 lemma det_ne_zero_of_sum_row_pos [DecidableEq n] {S : Type*} [LinearOrderedCommRing S]
-    {A : Matrix n n S} (h1 : ∀ i j, i ≠ j → A i j < 0) (h2 : ∀ i, 0 < ∑ j, A i j) :
+    {A : Matrix n n S} (h1 : Pairwise fun i j => A i j < 0) (h2 : ∀ i, 0 < ∑ j, A i j) :
     A.det ≠ 0 := by
   rw [← Matrix.det_transpose]
   refine det_ne_zero_of_sum_col_pos ?_ ?_
   · simp_rw [Matrix.transpose_apply]
-    exact fun i j h => h1 j i h.symm
+    exact fun i j h => h1 h.symm
   · simp_rw [Matrix.transpose_apply]
     exact h2
 

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -113,7 +113,7 @@ open Matrix
 /-- This holds for all integral domains (see `Matrix.exists_mulVec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type*} [DecidableEq n] [Field K] {M : Matrix n n K} :
-    (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
+    (∃ v ≠ 0, M.mulVec v = 0) ↔ M.det = 0 := by
   constructor
   · rintro ⟨v, hv, mul_eq⟩
     contrapose! hv
@@ -135,8 +135,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type*} [DecidableEq n] [Field K] {M :
 
 theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
-    (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
-  have : (∃ (v : _) (_ : v ≠ 0), mulVec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
+    (∃ v ≠ 0, M.mulVec v = 0) ↔ M.det = 0 := by
+  have : (∃ v ≠ 0, mulVec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
     exists_mulVec_eq_zero_iff_aux
   rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this
   refine' Iff.trans _ this; constructor <;> rintro ⟨v, hv, mul_eq⟩
@@ -169,19 +169,19 @@ theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [Comm
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
 theorem exists_mulVec_eq_zero_iff {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
+    {M : Matrix n n A} : (∃ v ≠ 0, M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
 theorem exists_vecMul_eq_zero_iff {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
+    {M : Matrix n n A} : (∃ v ≠ 0, M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mulVec_transpose] using exists_mulVec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
 
 theorem nondegenerate_iff_det_ne_zero {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : Nondegenerate M ↔ M.det ≠ 0 := by
-  refine' Iff.trans _ (not_iff_not.mpr exists_vecMul_eq_zero_iff)
-  simp only [not_exists]
+  rw [ne_eq, ← exists_vecMul_eq_zero_iff]
+  push_neg
   constructor
   · intro hM v hv hMv
     obtain ⟨w, hwMv⟩ := hM.exists_not_ortho_of_ne_zero hv

@@ -191,7 +191,7 @@ theorem nondegenerate_iff_det_ne_zero {A : Type*} [DecidableEq n] [CommRing A] [
     simpa only [dotProduct_mulVec, dotProduct_single, mul_one] using hv (Pi.single i 1)
 #align matrix.nondegenerate_iff_det_ne_zero Matrix.nondegenerate_iff_det_ne_zero
 
-alias nondegenerate_iff_det_ne_zero ↔ Nondegenerate.det_ne_zero Nondegenerate.of_det_ne_zero
+alias ⟨Nondegenerate.det_ne_zero, Nondegenerate.of_det_ne_zero⟩ := nondegenerate_iff_det_ne_zero
 #align matrix.nondegenerate.det_ne_zero Matrix.Nondegenerate.det_ne_zero
 #align matrix.nondegenerate.of_det_ne_zero Matrix.Nondegenerate.of_det_ne_zero
 

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

@@ -163,7 +163,7 @@ theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [Comm
             ((algebraMap A K).mapMatrix M).mulVec (algebraMap _ K b • v) i := ?_
         _ = 0 := ?_
         _ = algebraMap A K 0 := (RingHom.map_zero _).symm
-      · simp_rw [RingHom.map_mulVec, mulVec, dotProduct, Function.comp_apply, hf, Subtype.coe_mk,
+      · simp_rw [RingHom.map_mulVec, mulVec, dotProduct, Function.comp_apply, hf,
           RingHom.mapMatrix_apply, Pi.smul_apply, smul_eq_mul, Algebra.smul_def]
       · rw [mulVec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'

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

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

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

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

@@ -123,7 +123,7 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type*} [DecidableEq n] [Field K] {M :
     have : Function.Injective (Matrix.toLin' M) := by
       simpa only [← LinearMap.ker_eq_bot, ker_toLin'_eq_bot_iff, not_imp_not] using h
     have :
-      M ⬝
+      M *
           LinearMap.toMatrix'
             ((LinearEquiv.ofInjectiveEndo (Matrix.toLin' M) this).symm : (n → K) →ₗ[K] n → K) =
         1 := by

Prove Gershgorin circle theorem and some applications that will be useful for the proof of Dirichlet's unit theorem #5960

@@ -33,15 +33,16 @@ matrix, linear_equiv, determinant, inverse
 
 -/
 
+variable {n : Type*} [Fintype n]
 
 namespace Matrix
 
+section LinearEquiv
+
 open LinearMap
 
 variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
 
-variable {n : Type*} [Fintype n]
-
 section ToLinearEquiv'
 
 variable [DecidableEq n]
@@ -196,4 +197,52 @@ alias nondegenerate_iff_det_ne_zero ↔ Nondegenerate.det_ne_zero Nondegenerate.
 
 end Nondegenerate
 
+end LinearEquiv
+
+section Determinant
+
+open BigOperators
+
+/-- A matrix whose nondiagonal entries are negative with the sum of the entries of each
+column positive has nonzero determinant. -/
+lemma det_ne_zero_of_sum_col_pos [DecidableEq n] {S : Type*} [LinearOrderedCommRing S]
+    {A : Matrix n n S} (h1 : ∀ i j, i ≠ j → A i j < 0) (h2 : ∀ j, 0 < ∑ i, A i j) :
+    A.det ≠ 0 := by
+  cases isEmpty_or_nonempty n
+  · simp
+  · contrapose! h2
+    obtain ⟨v, ⟨h_vnz, h_vA⟩⟩ := Matrix.exists_vecMul_eq_zero_iff.mpr h2
+    wlog h_sup : 0 < Finset.sup' Finset.univ Finset.univ_nonempty v
+    · refine this h1 inferInstance h2 (-1 • v) ?_ ?_ ?_
+      · exact smul_ne_zero (by norm_num) h_vnz
+      · rw [Matrix.vecMul_smul, h_vA, smul_zero]
+      · obtain ⟨i, hi⟩ := Function.ne_iff.mp h_vnz
+        simp_rw [Finset.lt_sup'_iff, Finset.mem_univ, true_and] at h_sup ⊢
+        simp_rw [not_exists, not_lt] at h_sup
+        refine ⟨i, ?_⟩
+        rw [Pi.smul_apply, neg_smul, one_smul, Left.neg_pos_iff]
+        refine Ne.lt_of_le hi (h_sup i)
+    · obtain ⟨j₀, -, h_j₀⟩ := Finset.exists_mem_eq_sup' Finset.univ_nonempty v
+      refine ⟨j₀, ?_⟩
+      rw [← mul_le_mul_left (h_j₀ ▸ h_sup), Finset.mul_sum, mul_zero]
+      rw [show 0 = ∑ i, v i * A i j₀ from (congrFun h_vA j₀).symm]
+      refine Finset.sum_le_sum (fun i hi => ?_)
+      by_cases h : i = j₀
+      · rw [h]
+      · exact (mul_le_mul_right_of_neg (h1 i j₀ h)).mpr (h_j₀ ▸ Finset.le_sup' v hi)
+
+/-- A matrix whose nondiagonal entries are negative with the sum of the entries of each
+row positive has nonzero determinant. -/
+lemma det_ne_zero_of_sum_row_pos [DecidableEq n] {S : Type*} [LinearOrderedCommRing S]
+    {A : Matrix n n S} (h1 : ∀ i j, i ≠ j → A i j < 0) (h2 : ∀ i, 0 < ∑ j, A i j) :
+    A.det ≠ 0 := by
+  rw [← Matrix.det_transpose]
+  refine det_ne_zero_of_sum_col_pos ?_ ?_
+  · simp_rw [Matrix.transpose_apply]
+    exact fun i j h => h1 j i h.symm
+  · simp_rw [Matrix.transpose_apply]
+    exact h2
+
+end Determinant
+
 end Matrix

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

This has nice performance benefits.

@@ -38,9 +38,9 @@ namespace Matrix
 
 open LinearMap
 
-variable {R M : Type _} [CommRing R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
 
-variable {n : Type _} [Fintype n]
+variable {n : Type*} [Fintype n]
 
 section ToLinearEquiv'
 
@@ -111,7 +111,7 @@ open Matrix
 
 /-- This holds for all integral domains (see `Matrix.exists_mulVec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
-theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M : Matrix n n K} :
+theorem exists_mulVec_eq_zero_iff_aux {K : Type*} [DecidableEq n] [Field K] {M : Matrix n n K} :
     (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
   constructor
   · rintro ⟨v, hv, mul_eq⟩
@@ -132,7 +132,7 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
     exact Matrix.det_ne_zero_of_right_inverse this
 #align matrix.exists_mul_vec_eq_zero_iff_aux Matrix.exists_mulVec_eq_zero_iff_aux
 
-theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
+theorem exists_mulVec_eq_zero_iff' {A : Type*} (K : Type*) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
     (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
   have : (∃ (v : _) (_ : v ≠ 0), mulVec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
@@ -167,17 +167,17 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
       · rw [mulVec_smul, mul_eq, Pi.smul_apply, Pi.zero_apply, smul_zero]
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
-theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
+theorem exists_mulVec_eq_zero_iff {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
-theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
+theorem exists_vecMul_eq_zero_iff {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mulVec_transpose] using exists_mulVec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff
 
-theorem nondegenerate_iff_det_ne_zero {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
+theorem nondegenerate_iff_det_ne_zero {A : Type*} [DecidableEq n] [CommRing A] [IsDomain A]
     {M : Matrix n n A} : Nondegenerate M ↔ M.det ≠ 0 := by
   refine' Iff.trans _ (not_iff_not.mpr exists_vecMul_eq_zero_iff)
   simp only [not_exists]

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.to_linear_equiv
-! leanprover-community/mathlib commit e42cfdb03b7902f8787a1eb552cb8f77766b45b9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.FiniteDimensional
 import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup
@@ -16,6 +11,8 @@ import Mathlib.LinearAlgebra.Matrix.ToLin
 import Mathlib.RingTheory.Localization.FractionRing
 import Mathlib.RingTheory.Localization.Integer
 
+#align_import linear_algebra.matrix.to_linear_equiv from "leanprover-community/mathlib"@"e42cfdb03b7902f8787a1eb552cb8f77766b45b9"
+
 /-!
 # Matrices and linear equivalences
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -115,7 +115,7 @@ open Matrix
 /-- This holds for all integral domains (see `Matrix.exists_mulVec_eq_zero_iff`),
 not just fields, but it's easier to prove it for the field of fractions first. -/
 theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M : Matrix n n K} :
-    (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
+    (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
   constructor
   · rintro ⟨v, hv, mul_eq⟩
     contrapose! hv
@@ -137,8 +137,8 @@ theorem exists_mulVec_eq_zero_iff_aux {K : Type _} [DecidableEq n] [Field K] {M
 
 theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [CommRing A]
     [Nontrivial A] [Field K] [Algebra A K] [IsFractionRing A K] {M : Matrix n n A} :
-    (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
-  have : (∃ (v : _)(_ : v ≠ 0), mulVec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
+    (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 := by
+  have : (∃ (v : _) (_ : v ≠ 0), mulVec ((algebraMap A K).mapMatrix M) v = 0) ↔ _ :=
     exists_mulVec_eq_zero_iff_aux
   rw [← RingHom.map_det, IsFractionRing.to_map_eq_zero_iff] at this
   refine' Iff.trans _ this; constructor <;> rintro ⟨v, hv, mul_eq⟩
@@ -171,12 +171,12 @@ theorem exists_mulVec_eq_zero_iff' {A : Type _} (K : Type _) [DecidableEq n] [Co
 #align matrix.exists_mul_vec_eq_zero_iff' Matrix.exists_mulVec_eq_zero_iff'
 
 theorem exists_mulVec_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
+    {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.mulVec v = 0) ↔ M.det = 0 :=
   exists_mulVec_eq_zero_iff' (FractionRing A)
 #align matrix.exists_mul_vec_eq_zero_iff Matrix.exists_mulVec_eq_zero_iff
 
 theorem exists_vecMul_eq_zero_iff {A : Type _} [DecidableEq n] [CommRing A] [IsDomain A]
-    {M : Matrix n n A} : (∃ (v : _)(_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
+    {M : Matrix n n A} : (∃ (v : _) (_ : v ≠ 0), M.vecMul v = 0) ↔ M.det = 0 := by
   simpa only [← M.det_transpose, ← mulVec_transpose] using exists_mulVec_eq_zero_iff
 #align matrix.exists_vec_mul_eq_zero_iff Matrix.exists_vecMul_eq_zero_iff