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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
 import Data.Matrix.Basis
-import Data.Matrix.Dmatrix
+import Data.Matrix.DMatrix
 import LinearAlgebra.Matrix.Determinant
 import LinearAlgebra.Matrix.Reindex
 import Tactic.FieldSimp

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

@@ -478,7 +478,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
       by simp [list_transvec_col]
     simp only [Matrix.mul_assoc, A, Matrix.hMul_eq_hMul, List.prod_cons]
     by_cases h : n' = i
-    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h ; simp [h]
+    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h; simp [h]
       rw [h, transvection_mul_apply_same, IH, list_transvec_col_mul_last_row_drop _ _ hn, ← hni]
       field_simp [hM]
     · have hni : n ≠ i := by rintro rfl; cases i; simpa using h
@@ -552,7 +552,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
     simp only [List.take_succ, A, ← Matrix.mul_assoc, List.prod_append, Matrix.mul_one,
       Matrix.hMul_eq_hMul, List.prod_cons, List.prod_nil, Option.to_list_some]
     by_cases h : n' = i
-    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h ; simp only [h, coe_mk]
+    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h; simp only [h, coe_mk]
       have : ¬n.succ ≤ i := by simp only [← hni, n.lt_succ_self, not_le]
       simp only [h, mul_transvection_apply_same, List.take, if_false,
         mul_list_transvec_row_last_col_take _ _ hnr.le, hni.le, this, if_true, IH hnr.le]
@@ -651,8 +651,8 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
   -- when the last coefficient is zero but there is a nonzero coefficient on the last row or the
   -- last column, we will first put this nonzero coefficient in last position, and then argue as
   -- above.
-  push_neg at hM 
-  simp [not_and_or, is_two_block_diagonal, to_blocks₁₂, to_blocks₂₁, ← Matrix.ext_iff] at H 
+  push_neg at hM
+  simp [not_and_or, is_two_block_diagonal, to_blocks₁₂, to_blocks₂₁, ← Matrix.ext_iff] at H
   have : ∃ i : Fin r, M (inl i) (inr star) ≠ 0 ∨ M (inr star) (inl i) ≠ 0 :=
     by
     cases H
@@ -666,7 +666,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
   · let M' := transvection (inr Unit.unit) (inl i) 1 ⬝ M
     have hM' : M' (inr star) (inr star) ≠ 0 := by simpa [M', hM]
     rcases exists_is_two_block_diagonal_of_ne_zero M' hM' with ⟨L, L', hLL'⟩
-    rw [Matrix.mul_assoc] at hLL' 
+    rw [Matrix.mul_assoc] at hLL'
     refine' ⟨L ++ [⟨inr star, inl i, by simp, 1⟩], L', _⟩
     simp only [List.map_append, List.prod_append, Matrix.mul_one, to_matrix_mk, List.prod_cons,
       List.prod_nil, mul_eq_mul, List.map, Matrix.mul_assoc (L.map to_matrix).Prod]
@@ -755,7 +755,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
   induction' hn : Fintype.card n with r IH generalizing n M
   · refine' ⟨List.nil, List.nil, fun _ => 1, _⟩
     ext i j
-    rw [Fintype.card_eq_zero_iff] at hn 
+    rw [Fintype.card_eq_zero_iff] at hn
     exact hn.elim' i
   · have e : n ≃ Sum (Fin r) Unit :=
       by

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

@@ -3,11 +3,11 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Data.Matrix.Basis
-import Mathbin.Data.Matrix.Dmatrix
-import Mathbin.LinearAlgebra.Matrix.Determinant
-import Mathbin.LinearAlgebra.Matrix.Reindex
-import Mathbin.Tactic.FieldSimp
+import Data.Matrix.Basis
+import Data.Matrix.Dmatrix
+import LinearAlgebra.Matrix.Determinant
+import LinearAlgebra.Matrix.Reindex
+import Tactic.FieldSimp
 
 #align_import linear_algebra.matrix.transvection from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
 

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

@@ -476,7 +476,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
       (list_transvec_col M).nthLe n hn' =
         transvection (inl n') (inr star) (-M (inl n') (inr star) / M (inr star) (inr star)) :=
       by simp [list_transvec_col]
-    simp only [Matrix.mul_assoc, A, Matrix.mul_eq_mul, List.prod_cons]
+    simp only [Matrix.mul_assoc, A, Matrix.hMul_eq_hMul, List.prod_cons]
     by_cases h : n' = i
     · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h ; simp [h]
       rw [h, transvection_mul_apply_same, IH, list_transvec_col_mul_last_row_drop _ _ hn, ← hni]
@@ -507,7 +507,7 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
             (-M (inr Unit.unit) (inl k') / M (inr Unit.unit) (inr Unit.unit))) :=
       by simp only [list_transvec_row, List.ofFnNthVal, hkr, dif_pos, List.get?_ofFn]; rfl
     simp only [List.take_succ, ← Matrix.mul_assoc, this, List.prod_append, Matrix.mul_one,
-      Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
+      Matrix.hMul_eq_hMul, List.prod_cons, List.prod_nil, Option.to_list_some]
     rw [mul_transvection_apply_of_ne, IH hkr.le]
     simp only [Ne.def, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
@@ -550,7 +550,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
             (-M (inr Unit.unit) (inl n') / M (inr Unit.unit) (inr Unit.unit))) :=
       by simp only [list_transvec_row, List.ofFnNthVal, hnr, dif_pos, List.get?_ofFn]; rfl
     simp only [List.take_succ, A, ← Matrix.mul_assoc, List.prod_append, Matrix.mul_one,
-      Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
+      Matrix.hMul_eq_hMul, List.prod_cons, List.prod_nil, Option.to_list_some]
     by_cases h : n' = i
     · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h ; simp only [h, coe_mk]
       have : ¬n.succ ≤ i := by simp only [← hni, n.lt_succ_self, not_le]

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.transvection
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Matrix.Basis
 import Mathbin.Data.Matrix.Dmatrix
@@ -14,6 +9,8 @@ import Mathbin.LinearAlgebra.Matrix.Determinant
 import Mathbin.LinearAlgebra.Matrix.Reindex
 import Mathbin.Tactic.FieldSimp
 
+#align_import linear_algebra.matrix.transvection from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
 /-!
 # Transvections
 

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

@@ -109,7 +109,7 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
       transvection i j c :=
   by
   cases nonempty_fintype n
-  ext (a b)
+  ext a b
   by_cases ha : i = a; by_cases hb : j = b
   ·
     simp only [update_row_self, transvection, ha, hb, Pi.add_apply, std_basis_matrix.apply_same,
@@ -309,7 +309,7 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
     (t.sumInl p).toMatrix = fromBlocks t.toMatrix 0 0 1 :=
   by
   cases t
-  ext (a b)
+  ext a b
   cases a <;> cases b
   · by_cases h : a = b <;> simp [transvection_struct.sum_inl, transvection, h, std_basis_matrix]
   · simp [transvection_struct.sum_inl, transvection]
@@ -365,7 +365,7 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix :=
   by
   cases t
-  ext (a b)
+  ext a b
   simp only [reindex_equiv, transvection, mul_boole, Algebra.id.smul_eq_mul, to_matrix_mk,
     submatrix_apply, reindex_apply, DMatrix.add_apply, Pi.smul_apply, reindex_alg_equiv_apply]
   by_cases ha : e t_i = a <;> by_cases hb : e t_j = b <;> by_cases hab : a = b <;>
@@ -608,10 +608,10 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
     IsTwoBlockDiagonal ((listTransvecCol M).Prod ⬝ M ⬝ (listTransvecRow M).Prod) :=
   by
   constructor
-  · ext (i j)
+  · ext i j
     have : j = star := by simp only [eq_iff_true_of_subsingleton]
     simp [to_blocks₁₂, this, list_transvec_col_mul_mul_list_transvec_row_last_row M hM]
-  · ext (i j)
+  · ext i j
     have : i = star := by simp only [eq_iff_true_of_subsingleton]
     simp [to_blocks₂₁, this, list_transvec_col_mul_mul_list_transvec_row_last_col M hM]
 #align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
@@ -714,7 +714,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
     congr
     · exact hM.1
     · exact hM.2
-    · ext (⟨⟩⟨⟩); rw [hc, to_blocks₂₂, of_apply]; rfl
+    · ext ⟨⟩ ⟨⟩; rw [hc, to_blocks₂₂, of_apply]; rfl
   rw [this]
   simp [h₀]
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
@@ -757,7 +757,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
   by
   induction' hn : Fintype.card n with r IH generalizing n M
   · refine' ⟨List.nil, List.nil, fun _ => 1, _⟩
-    ext (i j)
+    ext i j
     rw [Fintype.card_eq_zero_iff] at hn 
     exact hn.elim' i
   · have e : n ≃ Sum (Fin r) Unit :=

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

@@ -93,12 +93,15 @@ def transvection (c : R) : Matrix n n R :=
 #align matrix.transvection Matrix.transvection
 -/
 
+#print Matrix.transvection_zero /-
 @[simp]
 theorem transvection_zero : transvection i j (0 : R) = 1 := by simp [transvection]
 #align matrix.transvection_zero Matrix.transvection_zero
+-/
 
 section
 
+#print Matrix.updateRow_eq_transvection /-
 /-- A transvection matrix is obtained from the identity by adding `c` times the `j`-th row to
 the `i`-th row. -/
 theorem updateRow_eq_transvection [Finite n] (c : R) :
@@ -120,45 +123,59 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
       Algebra.id.smul_eq_mul, Ne.def, not_false_iff, DMatrix.add_apply, Pi.smul_apply,
       MulZeroClass.mul_zero, false_and_iff]
 #align matrix.update_row_eq_transvection Matrix.updateRow_eq_transvection
+-/
 
 variable [Fintype n]
 
+#print Matrix.transvection_mul_transvection_same /-
 theorem transvection_mul_transvection_same (h : i ≠ j) (c d : R) :
     transvection i j c ⬝ transvection i j d = transvection i j (c + d) := by
   simp [transvection, Matrix.add_mul, Matrix.mul_add, h, h.symm, add_smul, add_assoc,
     std_basis_matrix_add]
 #align matrix.transvection_mul_transvection_same Matrix.transvection_mul_transvection_same
+-/
 
+#print Matrix.transvection_mul_apply_same /-
 @[simp]
 theorem transvection_mul_apply_same (b : n) (c : R) (M : Matrix n n R) :
     (transvection i j c ⬝ M) i b = M i b + c * M j b := by simp [transvection, Matrix.add_mul]
 #align matrix.transvection_mul_apply_same Matrix.transvection_mul_apply_same
+-/
 
+#print Matrix.mul_transvection_apply_same /-
 @[simp]
 theorem mul_transvection_apply_same (a : n) (c : R) (M : Matrix n n R) :
     (M ⬝ transvection i j c) a j = M a j + c * M a i := by
   simp [transvection, Matrix.mul_add, mul_comm]
 #align matrix.mul_transvection_apply_same Matrix.mul_transvection_apply_same
+-/
 
+#print Matrix.transvection_mul_apply_of_ne /-
 @[simp]
 theorem transvection_mul_apply_of_ne (a b : n) (ha : a ≠ i) (c : R) (M : Matrix n n R) :
     (transvection i j c ⬝ M) a b = M a b := by simp [transvection, Matrix.add_mul, ha]
 #align matrix.transvection_mul_apply_of_ne Matrix.transvection_mul_apply_of_ne
+-/
 
+#print Matrix.mul_transvection_apply_of_ne /-
 @[simp]
 theorem mul_transvection_apply_of_ne (a b : n) (hb : b ≠ j) (c : R) (M : Matrix n n R) :
     (M ⬝ transvection i j c) a b = M a b := by simp [transvection, Matrix.mul_add, hb]
 #align matrix.mul_transvection_apply_of_ne Matrix.mul_transvection_apply_of_ne
+-/
 
+#print Matrix.det_transvection_of_ne /-
 @[simp]
 theorem det_transvection_of_ne (h : i ≠ j) (c : R) : det (transvection i j c) = 1 := by
   rw [← update_row_eq_transvection i j, det_update_row_add_smul_self _ h, det_one]
 #align matrix.det_transvection_of_ne Matrix.det_transvection_of_ne
+-/
 
 end
 
 variable (R n)
 
+#print Matrix.TransvectionStruct /-
 /-- A structure containing all the information from which one can build a nontrivial transvection.
 This structure is easier to manipulate than transvections as one has a direct access to all the
 relevant fields. -/
@@ -168,6 +185,7 @@ structure TransvectionStruct where
   hij : i ≠ j
   c : R
 #align matrix.transvection_struct Matrix.TransvectionStruct
+-/
 
 instance [Nontrivial n] : Nonempty (TransvectionStruct n R) := by
   choose x y hxy using exists_pair_ne n; exact ⟨⟨x, y, hxy, 0⟩⟩
@@ -183,17 +201,22 @@ def toMatrix (t : TransvectionStruct n R) : Matrix n n R :=
 #align matrix.transvection_struct.to_matrix Matrix.TransvectionStruct.toMatrix
 -/
 
+#print Matrix.TransvectionStruct.toMatrix_mk /-
 @[simp]
 theorem toMatrix_mk (i j : n) (hij : i ≠ j) (c : R) :
     TransvectionStruct.toMatrix ⟨i, j, hij, c⟩ = transvection i j c :=
   rfl
 #align matrix.transvection_struct.to_matrix_mk Matrix.TransvectionStruct.toMatrix_mk
+-/
 
+#print Matrix.TransvectionStruct.det /-
 @[simp]
 protected theorem det [Fintype n] (t : TransvectionStruct n R) : det t.toMatrix = 1 :=
   det_transvection_of_ne _ _ t.hij _
 #align matrix.transvection_struct.det Matrix.TransvectionStruct.det
+-/
 
+#print Matrix.TransvectionStruct.det_toMatrix_prod /-
 @[simp]
 theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
     det (L.map toMatrix).Prod = 1 := by
@@ -201,7 +224,9 @@ theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
   · simp
   · simp [IH]
 #align matrix.transvection_struct.det_to_matrix_prod Matrix.TransvectionStruct.det_toMatrix_prod
+-/
 
+#print Matrix.TransvectionStruct.inv /-
 /-- The inverse of a `transvection_struct`, designed so that `t.inv.to_matrix` is the inverse of
 `t.to_matrix`. -/
 @[simps]
@@ -212,19 +237,25 @@ protected def inv (t : TransvectionStruct n R) : TransvectionStruct n R
   hij := t.hij
   c := -t.c
 #align matrix.transvection_struct.inv Matrix.TransvectionStruct.inv
+-/
 
 section
 
 variable [Fintype n]
 
+#print Matrix.TransvectionStruct.inv_mul /-
 theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 := by
   rcases t with ⟨⟩; simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mul
+-/
 
+#print Matrix.TransvectionStruct.mul_inv /-
 theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 := by
   rcases t with ⟨⟩; simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_inv
+-/
 
+#print Matrix.TransvectionStruct.reverse_inv_prod_mul_prod /-
 theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
     (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod ⬝ (L.map toMatrix).Prod = 1 :=
   by
@@ -237,7 +268,9 @@ theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
       by simpa [Matrix.mul_assoc]
     simpa [inv_mul] using IH
 #align matrix.transvection_struct.reverse_inv_prod_mul_prod Matrix.TransvectionStruct.reverse_inv_prod_mul_prod
+-/
 
+#print Matrix.TransvectionStruct.prod_mul_reverse_inv_prod /-
 theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
     (L.map toMatrix).Prod ⬝ (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod = 1 :=
   by
@@ -251,6 +284,7 @@ theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
       by simpa [Matrix.mul_assoc]
     simp_rw [IH, Matrix.mul_one, t.mul_inv]
 #align matrix.transvection_struct.prod_mul_reverse_inv_prod Matrix.TransvectionStruct.prod_mul_reverse_inv_prod
+-/
 
 end
 
@@ -258,6 +292,7 @@ variable (p)
 
 open Sum
 
+#print Matrix.TransvectionStruct.sumInl /-
 /-- Given a `transvection_struct` on `n`, define the corresponding `transvection_struct` on `n ⊕ p`
 using the identity on `p`. -/
 def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
@@ -267,7 +302,9 @@ def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
   hij := by simp [t.hij]
   c := t.c
 #align matrix.transvection_struct.sum_inl Matrix.TransvectionStruct.sumInl
+-/
 
+#print Matrix.TransvectionStruct.toMatrix_sumInl /-
 theorem toMatrix_sumInl (t : TransvectionStruct n R) :
     (t.sumInl p).toMatrix = fromBlocks t.toMatrix 0 0 1 :=
   by
@@ -279,7 +316,9 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
   · simp [transvection_struct.sum_inl, transvection]
   · by_cases h : a = b <;> simp [transvection_struct.sum_inl, transvection, h]
 #align matrix.transvection_struct.to_matrix_sum_inl Matrix.TransvectionStruct.toMatrix_sumInl
+-/
 
+#print Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul /-
 @[simp]
 theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
@@ -290,7 +329,9 @@ theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
   · simp
   · simp [Matrix.mul_assoc, IH, to_matrix_sum_inl, from_blocks_multiply]
 #align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul
+-/
 
+#print Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod /-
 @[simp]
 theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
@@ -301,9 +342,11 @@ theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
   · simp
   · simp [IH, to_matrix_sum_inl, from_blocks_multiply]
 #align matrix.transvection_struct.mul_sum_inl_to_matrix_prod Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod
+-/
 
 variable {p}
 
+#print Matrix.TransvectionStruct.reindexEquiv /-
 /-- Given a `transvection_struct` on `n` and an equivalence between `n` and `p`, define the
 corresponding `transvection_struct` on `p`. -/
 def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct p R
@@ -313,9 +356,11 @@ def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct
   hij := by simp [t.hij]
   c := t.c
 #align matrix.transvection_struct.reindex_equiv Matrix.TransvectionStruct.reindexEquiv
+-/
 
 variable [Fintype n] [Fintype p]
 
+#print Matrix.TransvectionStruct.toMatrix_reindexEquiv /-
 theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix :=
   by
@@ -326,7 +371,9 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
   by_cases ha : e t_i = a <;> by_cases hb : e t_j = b <;> by_cases hab : a = b <;>
     simp [ha, hb, hab, ← e.apply_eq_iff_eq_symm_apply, std_basis_matrix]
 #align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquiv
+-/
 
+#print Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod /-
 theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n R)) :
     (L.map (toMatrix ∘ reindexEquiv e)).Prod = reindexAlgEquiv R e (L.map toMatrix).Prod :=
   by
@@ -336,6 +383,7 @@ theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n
       reindex_alg_equiv_apply, List.map]
     exact (reindex_alg_equiv_mul _ _ _ _).symm
 #align matrix.transvection_struct.to_matrix_reindex_equiv_prod Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod
+-/
 
 end TransvectionStruct
 
@@ -381,6 +429,7 @@ def listTransvecRow : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
 #align matrix.pivot.list_transvec_row Matrix.Pivot.listTransvecRow
 -/
 
+#print Matrix.Pivot.listTransvecCol_mul_last_row_drop /-
 /-- Multiplying by some of the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (((listTransvecCol M).drop k).Prod ⬝ M) (inr unit) i = M (inr unit) i :=
@@ -394,13 +443,17 @@ theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     rw [← List.cons_nthLe_drop_succ hn']
     simpa [list_transvec_col, Matrix.mul_assoc]
 #align matrix.pivot.list_transvec_col_mul_last_row_drop Matrix.Pivot.listTransvecCol_mul_last_row_drop
+-/
 
+#print Matrix.Pivot.listTransvecCol_mul_last_row /-
 /-- Multiplying by all the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row (i : Sum (Fin r) Unit) :
     ((listTransvecCol M).Prod ⬝ M) (inr unit) i = M (inr unit) i := by
   simpa using list_transvec_col_mul_last_row_drop M i (zero_le _)
 #align matrix.pivot.list_transvec_col_mul_last_row Matrix.Pivot.listTransvecCol_mul_last_row
+-/
 
+#print Matrix.Pivot.listTransvecCol_mul_last_col /-
 /-- Multiplying by all the matrices in `list_transvec_col M` kills all the coefficients in the
 last column but the last one. -/
 theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
@@ -440,7 +493,9 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         · simpa only [hni.symm, not_le, or_false_iff] using Nat.lt_succ_iff_lt_or_eq.1 hi
         · simpa only [not_le] using hi
 #align matrix.pivot.list_transvec_col_mul_last_col Matrix.Pivot.listTransvecCol_mul_last_col
+-/
 
+#print Matrix.Pivot.mul_listTransvecRow_last_col_take /-
 /-- Multiplying by some of the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (M ⬝ ((listTransvecRow M).take k).Prod) i (inr unit) = M i (inr unit) :=
@@ -459,7 +514,9 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     rw [mul_transvection_apply_of_ne, IH hkr.le]
     simp only [Ne.def, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
+-/
 
+#print Matrix.Pivot.mul_listTransvecRow_last_col /-
 /-- Multiplying by all the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
     (M ⬝ (listTransvecRow M).Prod) i (inr unit) = M i (inr unit) :=
@@ -468,7 +525,9 @@ theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
   rw [← List.take_length (list_transvec_row M), A]
   simpa using mul_list_transvec_row_last_col_take M i le_rfl
 #align matrix.pivot.mul_list_transvec_row_last_col Matrix.Pivot.mul_listTransvecRow_last_col
+-/
 
+#print Matrix.Pivot.mul_listTransvecRow_last_row /-
 /-- Multiplying by all the matrices in `list_transvec_row M` kills all the coefficients in the
 last row but the last one. -/
 theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
@@ -509,7 +568,9 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         · simpa only [not_le] using hi
         · simpa only [hni.symm, not_le, or_false_iff] using Nat.lt_succ_iff_lt_or_eq.1 hi
 #align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_row
+-/
 
+#print Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col /-
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last row but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr unit) ≠ 0)
@@ -522,7 +583,9 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr
   apply mul_list_transvec_row_last_row
   simpa [list_transvec_col_mul_last_row] using hM
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col
+-/
 
+#print Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row /-
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last column but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0)
@@ -535,7 +598,9 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr
   apply list_transvec_col_mul_last_col
   simpa [mul_list_transvec_row_last_col] using hM
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row
+-/
 
+#print Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow /-
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` turns
 the matrix in block-diagonal form. -/
 theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
@@ -550,7 +615,9 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
     have : i = star := by simp only [eq_iff_true_of_subsingleton]
     simp [to_blocks₂₁, this, list_transvec_col_mul_mul_list_transvec_row_last_col M hM]
 #align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
+-/
 
+#print Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero /-
 /-- There exist two lists of `transvection_struct` such that multiplying by them on the left and
 on the right makes a matrix block-diagonal, when the last coefficient is nonzero. -/
 theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0) :
@@ -569,6 +636,7 @@ theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0
   rw [A, B]
   exact is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row M hM
 #align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec /-
@@ -654,6 +722,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
 
 variable {n p} [Fintype n] [Fintype p]
 
+#print Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal /-
 /-- Reduction to diagonal form by elementary operations is invariant under reindexing. -/
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)
     (e : p ≃ n)
@@ -674,6 +743,7 @@ theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matr
   simp only [← reindex_alg_equiv_apply, ← reindex_alg_equiv_mul, h₀]
   simp only [Equiv.symm_symm, reindex_apply, submatrix_diagonal_equiv, reindex_alg_equiv_apply]
 #align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal
+-/
 
 #print Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux /-
 /-- Any matrix can be reduced to diagonal form by elementary operations. Formulated here on `Type 0`
@@ -703,6 +773,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
 -/
 
+#print Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal /-
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
@@ -712,7 +783,9 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
   apply reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal M e
   apply exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal
+-/
 
+#print Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec /-
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
 transvections.-/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
@@ -728,6 +801,7 @@ theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜
     by simpa [← h, Matrix.mul_assoc]
   rw [reverse_inv_prod_mul_prod, prod_mul_reverse_inv_prod, Matrix.one_mul, Matrix.mul_one]
 #align matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec
+-/
 
 end Pivot
 
@@ -735,6 +809,7 @@ open Pivot TransvectionStruct
 
 variable {n} [Fintype n]
 
+#print Matrix.diagonal_transvection_induction /-
 /-- Induction principle for matrices based on transvections: if a property is true for all diagonal
 matrices, all transvections, and is stable under product, then it is true for all matrices. This is
 the useful way to say that matrices are generated by diagonal matrices and transvections.
@@ -764,7 +839,9 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
   · simp only [Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map] at IH ⊢
     exact hmul _ _ (htransvec _) IH
 #align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_induction
+-/
 
+#print Matrix.diagonal_transvection_induction_of_det_ne_zero /-
 /-- Induction principle for invertible matrices based on transvections: if a property is true for
 all invertible diagonal matrices, all transvections, and is stable under product of invertible
 matrices, then it is true for all invertible matrices. This is the useful way to say that
@@ -786,6 +863,7 @@ theorem diagonal_transvection_induction_of_det_ne_zero (P : Matrix n n 𝕜 →
       exact ⟨by simp [QA.1, QB.1], hmul A B QA.1 QB.1 QA.2 QB.2⟩
   exact this.2
 #align matrix.diagonal_transvection_induction_of_det_ne_zero Matrix.diagonal_transvection_induction_of_det_ne_zero
+-/
 
 end Matrix
 

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

@@ -586,7 +586,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
   -- when the last coefficient is zero but there is a nonzero coefficient on the last row or the
   -- last column, we will first put this nonzero coefficient in last position, and then argue as
   -- above.
-  push_neg  at hM 
+  push_neg at hM 
   simp [not_and_or, is_two_block_diagonal, to_blocks₁₂, to_blocks₂₁, ← Matrix.ext_iff] at H 
   have : ∃ i : Fin r, M (inl i) (inr star) ≠ 0 ∨ M (inr star) (inl i) ≠ 0 :=
     by
@@ -694,7 +694,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
       by
       refine' Fintype.equivOfCardEq _
       rw [hn]
-      convert(@Fintype.card_sum (Fin r) Unit _ _).symm
+      convert (@Fintype.card_sum (Fin r) Unit _ _).symm
       simp
     apply reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal M e
     apply

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

@@ -428,7 +428,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
       by simp [list_transvec_col]
     simp only [Matrix.mul_assoc, A, Matrix.mul_eq_mul, List.prod_cons]
     by_cases h : n' = i
-    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h; simp [h]
+    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h ; simp [h]
       rw [h, transvection_mul_apply_same, IH, list_transvec_col_mul_last_row_drop _ _ hn, ← hni]
       field_simp [hM]
     · have hni : n ≠ i := by rintro rfl; cases i; simpa using h
@@ -496,7 +496,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
     simp only [List.take_succ, A, ← Matrix.mul_assoc, List.prod_append, Matrix.mul_one,
       Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
     by_cases h : n' = i
-    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h; simp only [h, coe_mk]
+    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h ; simp only [h, coe_mk]
       have : ¬n.succ ≤ i := by simp only [← hni, n.lt_succ_self, not_le]
       simp only [h, mul_transvection_apply_same, List.take, if_false,
         mul_list_transvec_row_last_col_take _ _ hnr.le, hni.le, this, if_true, IH hnr.le]
@@ -586,8 +586,8 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
   -- when the last coefficient is zero but there is a nonzero coefficient on the last row or the
   -- last column, we will first put this nonzero coefficient in last position, and then argue as
   -- above.
-  push_neg  at hM
-  simp [not_and_or, is_two_block_diagonal, to_blocks₁₂, to_blocks₂₁, ← Matrix.ext_iff] at H
+  push_neg  at hM 
+  simp [not_and_or, is_two_block_diagonal, to_blocks₁₂, to_blocks₂₁, ← Matrix.ext_iff] at H 
   have : ∃ i : Fin r, M (inl i) (inr star) ≠ 0 ∨ M (inr star) (inl i) ≠ 0 :=
     by
     cases H
@@ -601,7 +601,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
   · let M' := transvection (inr Unit.unit) (inl i) 1 ⬝ M
     have hM' : M' (inr star) (inr star) ≠ 0 := by simpa [M', hM]
     rcases exists_is_two_block_diagonal_of_ne_zero M' hM' with ⟨L, L', hLL'⟩
-    rw [Matrix.mul_assoc] at hLL'
+    rw [Matrix.mul_assoc] at hLL' 
     refine' ⟨L ++ [⟨inr star, inl i, by simp, 1⟩], L', _⟩
     simp only [List.map_append, List.prod_append, Matrix.mul_one, to_matrix_mk, List.prod_cons,
       List.prod_nil, mul_eq_mul, List.map, Matrix.mul_assoc (L.map to_matrix).Prod]
@@ -622,10 +622,10 @@ diagonal form by elementary operations, then one deduces it for matrices over `f
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
     (IH :
       ∀ M : Matrix (Fin r) (Fin r) 𝕜,
-        ∃ (L₀ L₀' : List (TransvectionStruct (Fin r) 𝕜))(D₀ : Fin r → 𝕜),
+        ∃ (L₀ L₀' : List (TransvectionStruct (Fin r) 𝕜)) (D₀ : Fin r → 𝕜),
           (L₀.map toMatrix).Prod ⬝ M ⬝ (L₀'.map toMatrix).Prod = diagonal D₀)
     (M : Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
-    ∃ (L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜))(D : Sum (Fin r) Unit → 𝕜),
+    ∃ (L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜)) (D : Sum (Fin r) Unit → 𝕜),
       (L.map toMatrix).Prod ⬝ M ⬝ (L'.map toMatrix).Prod = diagonal D :=
   by
   rcases exists_is_two_block_diagonal_list_transvec_mul_mul_list_transvec M with ⟨L₁, L₁', hM⟩
@@ -658,10 +658,10 @@ variable {n p} [Fintype n] [Fintype p]
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)
     (e : p ≃ n)
     (H :
-      ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+      ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
         (L.map toMatrix).Prod ⬝ Matrix.reindexAlgEquiv 𝕜 e M ⬝ (L'.map toMatrix).Prod =
           diagonal D) :
-    ∃ (L L' : List (TransvectionStruct p 𝕜))(D : p → 𝕜),
+    ∃ (L L' : List (TransvectionStruct p 𝕜)) (D : p → 𝕜),
       (L.map toMatrix).Prod ⬝ M ⬝ (L'.map toMatrix).Prod = diagonal D :=
   by
   rcases H with ⟨L₀, L₀', D₀, h₀⟩
@@ -682,13 +682,13 @@ See `exists_list_transvec_mul_mul_list_transvec_eq_diagonal` for the general ver
 from this one and reindexing). -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [Fintype n]
     [DecidableEq n] (M : Matrix n n 𝕜) :
-    ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+    ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       (L.map toMatrix).Prod ⬝ M ⬝ (L'.map toMatrix).Prod = diagonal D :=
   by
   induction' hn : Fintype.card n with r IH generalizing n M
   · refine' ⟨List.nil, List.nil, fun _ => 1, _⟩
     ext (i j)
-    rw [Fintype.card_eq_zero_iff] at hn
+    rw [Fintype.card_eq_zero_iff] at hn 
     exact hn.elim' i
   · have e : n ≃ Sum (Fin r) Unit :=
       by
@@ -705,7 +705,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
 
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
-    ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+    ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       (L.map toMatrix).Prod ⬝ M ⬝ (L'.map toMatrix).Prod = diagonal D :=
   by
   have e : n ≃ Fin (Fintype.card n) := Fintype.equivOfCardEq (by simp)
@@ -716,7 +716,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
 transvections.-/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
-    ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+    ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       M = (L.map toMatrix).Prod ⬝ diagonal D ⬝ (L'.map toMatrix).Prod :=
   by
   rcases exists_list_transvec_mul_mul_list_transvec_eq_diagonal M with ⟨L, L', D, h⟩
@@ -761,7 +761,7 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
     · simp only [← Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map]
       apply IH
       exact hmul _ _ PE (htransvec _)
-  · simp only [Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map] at IH⊢
+  · simp only [Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map] at IH ⊢
     exact hmul _ _ (htransvec _) IH
 #align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_induction
 

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

@@ -71,7 +71,7 @@ universe u₁ u₂
 
 namespace Matrix
 
-open Matrix
+open scoped Matrix
 
 variable (n p : Type _) (R : Type u₂) {𝕜 : Type _} [Field 𝕜]
 

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

@@ -93,24 +93,12 @@ def transvection (c : R) : Matrix n n R :=
 #align matrix.transvection Matrix.transvection
 -/
 
-/- warning: matrix.transvection_zero -> Matrix.transvection_zero is a dubious translation:
-lean 3 declaration is
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 @[simp]
 theorem transvection_zero : transvection i j (0 : R) = 1 := by simp [transvection]
 #align matrix.transvection_zero Matrix.transvection_zero
 
 section
 
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 /-- A transvection matrix is obtained from the identity by adding `c` times the `j`-th row to
 the `i`-th row. -/
 theorem updateRow_eq_transvection [Finite n] (c : R) :
@@ -135,69 +123,33 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
 
 variable [Fintype n]
 
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 theorem transvection_mul_transvection_same (h : i ≠ j) (c d : R) :
     transvection i j c ⬝ transvection i j d = transvection i j (c + d) := by
   simp [transvection, Matrix.add_mul, Matrix.mul_add, h, h.symm, add_smul, add_assoc,
     std_basis_matrix_add]
 #align matrix.transvection_mul_transvection_same Matrix.transvection_mul_transvection_same
 
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 @[simp]
 theorem transvection_mul_apply_same (b : n) (c : R) (M : Matrix n n R) :
     (transvection i j c ⬝ M) i b = M i b + c * M j b := by simp [transvection, Matrix.add_mul]
 #align matrix.transvection_mul_apply_same Matrix.transvection_mul_apply_same
 
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 @[simp]
 theorem mul_transvection_apply_same (a : n) (c : R) (M : Matrix n n R) :
     (M ⬝ transvection i j c) a j = M a j + c * M a i := by
   simp [transvection, Matrix.mul_add, mul_comm]
 #align matrix.mul_transvection_apply_same Matrix.mul_transvection_apply_same
 
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 @[simp]
 theorem transvection_mul_apply_of_ne (a b : n) (ha : a ≠ i) (c : R) (M : Matrix n n R) :
     (transvection i j c ⬝ M) a b = M a b := by simp [transvection, Matrix.add_mul, ha]
 #align matrix.transvection_mul_apply_of_ne Matrix.transvection_mul_apply_of_ne
 
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 @[simp]
 theorem mul_transvection_apply_of_ne (a b : n) (hb : b ≠ j) (c : R) (M : Matrix n n R) :
     (M ⬝ transvection i j c) a b = M a b := by simp [transvection, Matrix.mul_add, hb]
 #align matrix.mul_transvection_apply_of_ne Matrix.mul_transvection_apply_of_ne
 
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 @[simp]
 theorem det_transvection_of_ne (h : i ≠ j) (c : R) : det (transvection i j c) = 1 := by
   rw [← update_row_eq_transvection i j, det_update_row_add_smul_self _ h, det_one]
@@ -207,12 +159,6 @@ end
 
 variable (R n)
 
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 /-- A structure containing all the information from which one can build a nontrivial transvection.
 This structure is easier to manipulate than transvections as one has a direct access to all the
 relevant fields. -/
@@ -237,35 +183,17 @@ def toMatrix (t : TransvectionStruct n R) : Matrix n n R :=
 #align matrix.transvection_struct.to_matrix Matrix.TransvectionStruct.toMatrix
 -/
 
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 @[simp]
 theorem toMatrix_mk (i j : n) (hij : i ≠ j) (c : R) :
     TransvectionStruct.toMatrix ⟨i, j, hij, c⟩ = transvection i j c :=
   rfl
 #align matrix.transvection_struct.to_matrix_mk Matrix.TransvectionStruct.toMatrix_mk
 
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 @[simp]
 protected theorem det [Fintype n] (t : TransvectionStruct n R) : det t.toMatrix = 1 :=
   det_transvection_of_ne _ _ t.hij _
 #align matrix.transvection_struct.det Matrix.TransvectionStruct.det
 
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 @[simp]
 theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
     det (L.map toMatrix).Prod = 1 := by
@@ -274,12 +202,6 @@ theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
   · simp [IH]
 #align matrix.transvection_struct.det_to_matrix_prod Matrix.TransvectionStruct.det_toMatrix_prod
 
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 /-- The inverse of a `transvection_struct`, designed so that `t.inv.to_matrix` is the inverse of
 `t.to_matrix`. -/
 @[simps]
@@ -295,32 +217,14 @@ section
 
 variable [Fintype n]
 
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 theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 := by
   rcases t with ⟨⟩; simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mul
 
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 theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 := by
   rcases t with ⟨⟩; simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_inv
 
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 theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
     (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod ⬝ (L.map toMatrix).Prod = 1 :=
   by
@@ -334,12 +238,6 @@ theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
     simpa [inv_mul] using IH
 #align matrix.transvection_struct.reverse_inv_prod_mul_prod Matrix.TransvectionStruct.reverse_inv_prod_mul_prod
 
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 theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
     (L.map toMatrix).Prod ⬝ (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod = 1 :=
   by
@@ -360,12 +258,6 @@ variable (p)
 
 open Sum
 
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 /-- Given a `transvection_struct` on `n`, define the corresponding `transvection_struct` on `n ⊕ p`
 using the identity on `p`. -/
 def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
@@ -376,12 +268,6 @@ def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
   c := t.c
 #align matrix.transvection_struct.sum_inl Matrix.TransvectionStruct.sumInl
 
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 theorem toMatrix_sumInl (t : TransvectionStruct n R) :
     (t.sumInl p).toMatrix = fromBlocks t.toMatrix 0 0 1 :=
   by
@@ -394,9 +280,6 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
   · by_cases h : a = b <;> simp [transvection_struct.sum_inl, transvection, h]
 #align matrix.transvection_struct.to_matrix_sum_inl Matrix.TransvectionStruct.toMatrix_sumInl
 
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-<too large>
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 @[simp]
 theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
@@ -408,9 +291,6 @@ theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
   · simp [Matrix.mul_assoc, IH, to_matrix_sum_inl, from_blocks_multiply]
 #align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul
 
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 @[simp]
 theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
@@ -424,12 +304,6 @@ theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
 
 variable {p}
 
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 /-- Given a `transvection_struct` on `n` and an equivalence between `n` and `p`, define the
 corresponding `transvection_struct` on `p`. -/
 def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct p R
@@ -442,9 +316,6 @@ def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct
 
 variable [Fintype n] [Fintype p]
 
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 theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix :=
   by
@@ -456,9 +327,6 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     simp [ha, hb, hab, ← e.apply_eq_iff_eq_symm_apply, std_basis_matrix]
 #align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquiv
 
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 theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n R)) :
     (L.map (toMatrix ∘ reindexEquiv e)).Prod = reindexAlgEquiv R e (L.map toMatrix).Prod :=
   by
@@ -513,12 +381,6 @@ def listTransvecRow : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
 #align matrix.pivot.list_transvec_row Matrix.Pivot.listTransvecRow
 -/
 
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_row_drop Matrix.Pivot.listTransvecCol_mul_last_row_dropₓ'. -/
 /-- Multiplying by some of the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (((listTransvecCol M).drop k).Prod ⬝ M) (inr unit) i = M (inr unit) i :=
@@ -533,24 +395,12 @@ theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     simpa [list_transvec_col, Matrix.mul_assoc]
 #align matrix.pivot.list_transvec_col_mul_last_row_drop Matrix.Pivot.listTransvecCol_mul_last_row_drop
 
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 /-- Multiplying by all the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row (i : Sum (Fin r) Unit) :
     ((listTransvecCol M).Prod ⬝ M) (inr unit) i = M (inr unit) i := by
   simpa using list_transvec_col_mul_last_row_drop M i (zero_le _)
 #align matrix.pivot.list_transvec_col_mul_last_row Matrix.Pivot.listTransvecCol_mul_last_row
 
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_col Matrix.Pivot.listTransvecCol_mul_last_colₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_col M` kills all the coefficients in the
 last column but the last one. -/
 theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
@@ -591,12 +441,6 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         · simpa only [not_le] using hi
 #align matrix.pivot.list_transvec_col_mul_last_col Matrix.Pivot.listTransvecCol_mul_last_col
 
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_takeₓ'. -/
 /-- Multiplying by some of the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (M ⬝ ((listTransvecRow M).take k).Prod) i (inr unit) = M i (inr unit) :=
@@ -616,12 +460,6 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     simp only [Ne.def, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
 
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_col Matrix.Pivot.mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
     (M ⬝ (listTransvecRow M).Prod) i (inr unit) = M i (inr unit) :=
@@ -631,12 +469,6 @@ theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
   simpa using mul_list_transvec_row_last_col_take M i le_rfl
 #align matrix.pivot.mul_list_transvec_row_last_col Matrix.Pivot.mul_listTransvecRow_last_col
 
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_row M` kills all the coefficients in the
 last row but the last one. -/
 theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
@@ -678,9 +510,6 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         · simpa only [hni.symm, not_le, or_false_iff] using Nat.lt_succ_iff_lt_or_eq.1 hi
 #align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_row
 
-/- warning: matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col -> Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last row but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr unit) ≠ 0)
@@ -694,9 +523,6 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr
   simpa [list_transvec_col_mul_last_row] using hM
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col
 
-/- warning: matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row -> Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last column but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0)
@@ -710,12 +536,6 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr
   simpa [mul_list_transvec_row_last_col] using hM
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row
 
-/- warning: matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row -> Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))))
-Case conversion may be inaccurate. Consider using '#align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` turns
 the matrix in block-diagonal form. -/
 theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
@@ -731,9 +551,6 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
     simp [to_blocks₂₁, this, list_transvec_col_mul_mul_list_transvec_row_last_col M hM]
 #align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
 
-/- warning: matrix.pivot.exists_is_two_block_diagonal_of_ne_zero -> Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zeroₓ'. -/
 /-- There exist two lists of `transvection_struct` such that multiplying by them on the left and
 on the right makes a matrix block-diagonal, when the last coefficient is nonzero. -/
 theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0) :
@@ -837,9 +654,6 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
 
 variable {n p} [Fintype n] [Fintype p]
 
-/- warning: matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal -> Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Reduction to diagonal form by elementary operations is invariant under reindexing. -/
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)
     (e : p ≃ n)
@@ -889,12 +703,6 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
 -/
 
-/- warning: matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal -> Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
@@ -905,12 +713,6 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
   apply exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal
 
-/- warning: matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec -> Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvecₓ'. -/
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
 transvections.-/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
@@ -933,12 +735,6 @@ open Pivot TransvectionStruct
 
 variable {n} [Fintype n]
 
-/- warning: matrix.diagonal_transvection_induction -> Matrix.diagonal_transvection_induction is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_inductionₓ'. -/
 /-- Induction principle for matrices based on transvections: if a property is true for all diagonal
 matrices, all transvections, and is stable under product, then it is true for all matrices. This is
 the useful way to say that matrices are generated by diagonal matrices and transvections.
@@ -969,12 +765,6 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
     exact hmul _ _ (htransvec _) IH
 #align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_induction
 
-/- warning: matrix.diagonal_transvection_induction_of_det_ne_zero -> Matrix.diagonal_transvection_induction_of_det_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (P : (Matrix.{u1, u1, u2} n n 𝕜) -> Prop) (M : Matrix.{u1, u1, u2} n n 𝕜), (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) 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_1))))))))))) -> (forall (D : n -> 𝕜), (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D)) (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_1))))))))))) -> (P (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D))) -> (forall (t : Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))), P (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) t)) -> (forall (A : Matrix.{u1, u1, u2} n n 𝕜) (B : Matrix.{u1, u1, u2} n n 𝕜), (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) A) (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_1))))))))))) -> (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) B) (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_1))))))))))) -> (P A) -> (P B) -> (P (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) A B))) -> (P M)
-but is expected to have type
-  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (P : (Matrix.{u2, u2, u1} n n 𝕜) -> Prop) (M : Matrix.{u2, u2, u1} n n 𝕜), (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) M) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (D : n -> 𝕜), (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (P (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D))) -> (forall (t : Matrix.TransvectionStruct.{u1, u2} n 𝕜), P (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) t)) -> (forall (A : Matrix.{u2, u2, u1} n n 𝕜) (B : Matrix.{u2, u2, u1} n n 𝕜), (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) A) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) B) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (P A) -> (P B) -> (P (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) A B))) -> (P M)
-Case conversion may be inaccurate. Consider using '#align matrix.diagonal_transvection_induction_of_det_ne_zero Matrix.diagonal_transvection_induction_of_det_ne_zeroₓ'. -/
 /-- Induction principle for invertible matrices based on transvections: if a property is true for
 all invertible diagonal matrices, all transvections, and is stable under product of invertible
 matrices, then it is true for all invertible matrices. This is the useful way to say that

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

@@ -223,10 +223,8 @@ structure TransvectionStruct where
   c : R
 #align matrix.transvection_struct Matrix.TransvectionStruct
 
-instance [Nontrivial n] : Nonempty (TransvectionStruct n R) :=
-  by
-  choose x y hxy using exists_pair_ne n
-  exact ⟨⟨x, y, hxy, 0⟩⟩
+instance [Nontrivial n] : Nonempty (TransvectionStruct n R) := by
+  choose x y hxy using exists_pair_ne n; exact ⟨⟨x, y, hxy, 0⟩⟩
 
 namespace TransvectionStruct
 
@@ -303,10 +301,8 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4 t)) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mulₓ'. -/
-theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 :=
-  by
-  rcases t with ⟨⟩
-  simp [to_matrix, transvection_mul_transvection_same, t_hij]
+theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 := by
+  rcases t with ⟨⟩; simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mul
 
 /- warning: matrix.transvection_struct.mul_inv -> Matrix.TransvectionStruct.mul_inv is a dubious translation:
@@ -315,10 +311,8 @@ lean 3 declaration is
 but is expected to have type
   forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4 t))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_invₓ'. -/
-theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 :=
-  by
-  rcases t with ⟨⟩
-  simp [to_matrix, transvection_mul_transvection_same, t_hij]
+theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 := by
+  rcases t with ⟨⟩; simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_inv
 
 /- warning: matrix.transvection_struct.reverse_inv_prod_mul_prod -> Matrix.TransvectionStruct.reverse_inv_prod_mul_prod is a dubious translation:
@@ -584,16 +578,10 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
       by simp [list_transvec_col]
     simp only [Matrix.mul_assoc, A, Matrix.mul_eq_mul, List.prod_cons]
     by_cases h : n' = i
-    · have hni : n = i := by
-        cases i
-        simp only [Fin.mk_eq_mk] at h
-        simp [h]
+    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h; simp [h]
       rw [h, transvection_mul_apply_same, IH, list_transvec_col_mul_last_row_drop _ _ hn, ← hni]
       field_simp [hM]
-    · have hni : n ≠ i := by
-        rintro rfl
-        cases i
-        simpa using h
+    · have hni : n ≠ i := by rintro rfl; cases i; simpa using h
       simp only [transvection_mul_apply_of_ne, Ne.def, not_false_iff, Ne.symm h]
       rw [IH]
       rcases le_or_lt (n + 1) i with (hi | hi)
@@ -621,9 +609,7 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
       (list_transvec_row M).get? k =
         ↑(transvection (inr Unit.unit) (inl k')
             (-M (inr Unit.unit) (inl k') / M (inr Unit.unit) (inr Unit.unit))) :=
-      by
-      simp only [list_transvec_row, List.ofFnNthVal, hkr, dif_pos, List.get?_ofFn]
-      rfl
+      by simp only [list_transvec_row, List.ofFnNthVal, hkr, dif_pos, List.get?_ofFn]; rfl
     simp only [List.take_succ, ← Matrix.mul_assoc, this, List.prod_append, Matrix.mul_one,
       Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
     rw [mul_transvection_apply_of_ne, IH hkr.le]
@@ -674,24 +660,16 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
       (list_transvec_row M).get? n =
         ↑(transvection (inr Unit.unit) (inl n')
             (-M (inr Unit.unit) (inl n') / M (inr Unit.unit) (inr Unit.unit))) :=
-      by
-      simp only [list_transvec_row, List.ofFnNthVal, hnr, dif_pos, List.get?_ofFn]
-      rfl
+      by simp only [list_transvec_row, List.ofFnNthVal, hnr, dif_pos, List.get?_ofFn]; rfl
     simp only [List.take_succ, A, ← Matrix.mul_assoc, List.prod_append, Matrix.mul_one,
       Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
     by_cases h : n' = i
-    · have hni : n = i := by
-        cases i
-        simp only [Fin.mk_eq_mk] at h
-        simp only [h, coe_mk]
+    · have hni : n = i := by cases i; simp only [Fin.mk_eq_mk] at h; simp only [h, coe_mk]
       have : ¬n.succ ≤ i := by simp only [← hni, n.lt_succ_self, not_le]
       simp only [h, mul_transvection_apply_same, List.take, if_false,
         mul_list_transvec_row_last_col_take _ _ hnr.le, hni.le, this, if_true, IH hnr.le]
       field_simp [hM]
-    · have hni : n ≠ i := by
-        rintro rfl
-        cases i
-        simpa using h
+    · have hni : n ≠ i := by rintro rfl; cases i; simpa using h
       simp only [IH hnr.le, Ne.def, mul_transvection_apply_of_ne, not_false_iff, Ne.symm h]
       rcases le_or_lt (n + 1) i with (hi | hi)
       · simp [hi, n.le_succ.trans hi, if_true]
@@ -784,8 +762,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
     ∃ L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜),
       IsTwoBlockDiagonal ((L.map toMatrix).Prod ⬝ M ⬝ (L'.map toMatrix).Prod) :=
   by
-  by_cases H : is_two_block_diagonal M
-  · refine' ⟨List.nil, List.nil, by simpa using H⟩
+  by_cases H : is_two_block_diagonal M; · refine' ⟨List.nil, List.nil, by simpa using H⟩
   -- we have already proved this when the last coefficient is nonzero
   by_cases hM : M (inr star) (inr star) ≠ 0
   · exact exists_is_two_block_diagonal_of_ne_zero M hM
@@ -852,9 +829,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
     congr
     · exact hM.1
     · exact hM.2
-    · ext (⟨⟩⟨⟩)
-      rw [hc, to_blocks₂₂, of_apply]
-      rfl
+    · ext (⟨⟩⟨⟩); rw [hc, to_blocks₂₂, of_apply]; rfl
   rw [this]
   simp [h₀]
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
@@ -981,9 +956,7 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
   suffices H :
     ∀ (L₁ L₂ : List (transvection_struct n 𝕜)) (E : Matrix n n 𝕜),
       P E → P ((L₁.map to_matrix).Prod ⬝ E ⬝ (L₂.map to_matrix).Prod)
-  · rw [h]
-    apply H L L'
-    exact PD
+  · rw [h]; apply H L L'; exact PD
   intro L₁ L₂ E PE
   induction' L₁ with t L₁ IH
   · simp only [Matrix.one_mul, List.prod_nil, List.map]
@@ -1015,9 +988,7 @@ theorem diagonal_transvection_induction_of_det_ne_zero (P : Matrix n n 𝕜 →
   have : Q M := by
     apply diagonal_transvection_induction Q M
     · intro D hD
-      have detD : det (diagonal D) ≠ 0 := by
-        rw [hD]
-        exact hMdet
+      have detD : det (diagonal D) ≠ 0 := by rw [hD]; exact hMdet
       exact ⟨detD, hdiag _ detD⟩
     · intro t
       exact ⟨by simp, htransvec t⟩

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

@@ -401,10 +401,7 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
 #align matrix.transvection_struct.to_matrix_sum_inl Matrix.TransvectionStruct.toMatrix_sumInl
 
 /- warning: matrix.transvection_struct.sum_inl_to_matrix_prod_mul -> Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mulₓ'. -/
 @[simp]
 theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
@@ -418,10 +415,7 @@ theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
 #align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul
 
 /- warning: matrix.transvection_struct.mul_sum_inl_to_matrix_prod -> Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.mul_sum_inl_to_matrix_prod Matrix.TransvectionStruct.mul_sumInl_toMatrix_prodₓ'. -/
 @[simp]
 theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
@@ -455,10 +449,7 @@ def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct
 variable [Fintype n] [Fintype p]
 
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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquivₓ'. -/
 theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix :=
@@ -472,10 +463,7 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
 #align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquiv
 
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(CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv_prod Matrix.TransvectionStruct.toMatrix_reindexEquiv_prodₓ'. -/
 theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n R)) :
     (L.map (toMatrix ∘ reindexEquiv e)).Prod = reindexAlgEquiv R e (L.map toMatrix).Prod :=
@@ -713,10 +701,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
 #align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_row
 
 /- warning: matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col -> Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last row but the last one. -/
@@ -732,10 +717,7 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col
 
 /- warning: matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row -> Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last column but the last one. -/
@@ -772,10 +754,7 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
 #align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
 
 /- warning: matrix.pivot.exists_is_two_block_diagonal_of_ne_zero -> Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zeroₓ'. -/
 /-- There exist two lists of `transvection_struct` such that multiplying by them on the left and
 on the right makes a matrix block-diagonal, when the last coefficient is nonzero. -/
@@ -884,10 +863,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
 variable {n p} [Fintype n] [Fintype p]
 
 /- warning: matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal -> Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal is a dubious translation:
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_inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) 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(Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toZero.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) 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(Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u1 u3) u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AlgEquivClass.toAlgHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, max u1 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))))))) (Matrix.reindexAlgEquiv.{u3, u1, u2} p n 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D))))) -> (Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L' : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (p -> 𝕜) (fun (D : p -> 𝕜) => Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.mul.{u2, u3, u3, u3} p p p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u3, u3, u3} p p p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Reduction to diagonal form by elementary operations is invariant under reindexing. -/
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)

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

@@ -458,7 +458,7 @@ variable [Fintype n] [Fintype p]
 lean 3 declaration is
   forall {n : Type.{u2}} {p : Type.{u3}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u3} p] (e : Equiv.{succ u2, succ u3} n p) (t : Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4), Eq.{succ (max u3 u1)} (Matrix.{u3, u3, u1} p p R) (Matrix.TransvectionStruct.toMatrix.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4 (Matrix.TransvectionStruct.reindexEquiv.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4 e t)) (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgEquiv.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (fun (_x : AlgEquiv.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) => (Matrix.{u2, u2, u1} n n R) -> (Matrix.{u3, u3, u1} p p R)) (AlgEquiv.hasCoeToFun.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (Matrix.reindexAlgEquiv.{u2, u3, u1} n p R (CommRing.toCommSemiring.{u1} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t))
 but is expected to have type
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_inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) 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: p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) 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(CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t))
+  forall {n : Type.{u2}} {p : Type.{u1}} {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (e : Equiv.{succ u2, succ u1} n p) (t : Matrix.TransvectionStruct.{u3, u2} n R), Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} p p R) (Matrix.TransvectionStruct.toMatrix.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4 (Matrix.TransvectionStruct.reindexEquiv.{u3, u2, u1} n p R e t)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), max (succ u3) (succ u1)} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R 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(Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (SMulZeroClass.toSMul.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquivₓ'. -/
 theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix :=
@@ -475,7 +475,7 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
 lean 3 declaration is
   forall {n : Type.{u2}} {p : Type.{u3}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u3} p] (e : Equiv.{succ u2, succ u3} n p) (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)), Eq.{succ (max u3 u1)} (Matrix.{u3, u3, u1} p p R) (List.prod.{max u3 u1} (Matrix.{u3, u3, u1} p p R) (Matrix.hasMul.{u1, u3} p R _inst_6 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u3 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u3, u3, u1} p p R) (Function.comp.{succ (max u2 u1), max (succ u3) (succ u1), succ (max u3 u1)} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4) (Matrix.{u3, u3, u1} p p R) (Matrix.TransvectionStruct.toMatrix.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4) (Matrix.TransvectionStruct.reindexEquiv.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4 e)) L)) (coeFn.{max (succ (max u2 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(CommRing.toCommSemiring.{u1} R _inst_4)))) (fun (_x : AlgEquiv.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) => (Matrix.{u2, u2, u1} n n R) -> (Matrix.{u3, u3, u1} p p R)) (AlgEquiv.hasCoeToFun.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (Matrix.reindexAlgEquiv.{u2, u3, u1} n p R (CommRing.toCommSemiring.{u1} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
 but is expected to have type
-  forall {n : Type.{u2}} {p : Type.{u1}} {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (e : Equiv.{succ u2, succ u1} n p) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)), Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} p p R) (List.prod.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.instMulMatrix.{u3, u1} p R _inst_6 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (Matrix.{u2, u2, u3} n n R) (fun (_x : Matrix.{u2, u2, u3} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u3} n n R) => Matrix.{u1, u1, u3} p p R) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (SMulZeroClass.toSMul.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
+  forall {n : Type.{u2}} {p : Type.{u1}} {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (e : Equiv.{succ u2, succ u1} n p) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)), Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} p p R) (List.prod.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.instMulMatrix.{u3, u1} p R _inst_6 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u1 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u1, u1, u3} p p R) (Function.comp.{succ (max u2 u3), max (succ u1) (succ u3), succ (max u1 u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, u1} p R) (Matrix.{u1, u1, u3} p p R) (Matrix.TransvectionStruct.toMatrix.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4) (Matrix.TransvectionStruct.reindexEquiv.{u3, u2, u1} n p R e)) L)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), max (succ u3) (succ u1)} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R 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R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv_prod Matrix.TransvectionStruct.toMatrix_reindexEquiv_prodₓ'. -/
 theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n R)) :
     (L.map (toMatrix ∘ reindexEquiv e)).Prod = reindexAlgEquiv R e (L.map toMatrix).Prod :=
@@ -887,7 +887,7 @@ variable {n p} [Fintype n] [Fintype p]
 lean 3 declaration is
   forall {n : Type.{u1}} {p : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : Field.{u3} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u2} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u2} p] (M : Matrix.{u2, u2, u3} p p 𝕜) (e : Equiv.{succ u2, succ u1} p n), (Exists.{succ (max u1 u3)} (List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L : List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{succ (max u1 u3)} (List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u3)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u3)} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.mul.{u3, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))))) (Matrix.mul.{u3, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))))) (List.prod.{max u1 u3} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.hasMul.{u3, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u3} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u3} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u3} 𝕜 (Ring.toAddCommGroupWithOne.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (List.map.{max u1 u3, max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) L)) (coeFn.{max (succ (max u2 u3)) (succ (max u1 u3)), max (succ (max u2 u3)) (succ (max u1 u3))} (AlgEquiv.{u3, max u2 u3, max u1 u3} 𝕜 (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.{u1, u1, u3} n n 𝕜) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (Matrix.semiring.{u3, u2} p 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u3, u1} n 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u3, u2, u3} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)))) (Matrix.algebra.{u3, u1, u3} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))))) (fun (_x : AlgEquiv.{u3, max u2 u3, max u1 u3} 𝕜 (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.{u1, u1, u3} n n 𝕜) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (Matrix.semiring.{u3, u2} p 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u3, u1} n 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u3, u2, u3} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)))) (Matrix.algebra.{u3, u1, u3} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))))) => (Matrix.{u2, u2, u3} p p 𝕜) -> (Matrix.{u1, u1, u3} n n 𝕜)) (AlgEquiv.hasCoeToFun.{u3, max u2 u3, max u1 u3} 𝕜 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𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} p n 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u3} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.hasMul.{u3, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) D))))) -> (Exists.{succ (max u2 u3)} (List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{succ (max u2 u3)} (List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L' : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{max 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(Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u3} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u3} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u3} 𝕜 (Ring.toAddCommGroupWithOne.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) L)) M) (List.prod.{max u2 u3} (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.hasMul.{u3, u2} p 𝕜 _inst_6 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u3} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u3} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u3} 𝕜 (Ring.toAddCommGroupWithOne.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) D)))))
 but is expected to have type
-  forall {n : Type.{u1}} {p : Type.{u3}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u3, u3, u2} p p 𝕜) (e : Equiv.{succ u3, succ u1} p n), (Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) 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(CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Matrix.{u3, u3, u2} p p 𝕜) (fun (_x : Matrix.{u3, u3, u2} p p 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u3, u3, u2} p p 𝕜) => Matrix.{u1, u1, u2} n n 𝕜) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (SMulZeroClass.toSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toZero.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u1 u3) u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AlgEquivClass.toAlgHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, max u1 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))))))) (Matrix.reindexAlgEquiv.{u3, u1, u2} p n 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D))))) -> (Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L' : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (p -> 𝕜) (fun (D : p -> 𝕜) => Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.mul.{u2, u3, u3, u3} p p p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 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(Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D)))))
+  forall {n : Type.{u1}} {p : Type.{u3}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u3, u3, u2} p p 𝕜) (e : Equiv.{succ u3, succ u1} p n), (Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toZero.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u1 u3) u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AlgEquivClass.toAlgHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, max u1 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))))))) (Matrix.reindexAlgEquiv.{u3, u1, u2} p n 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D)))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Reduction to diagonal form by elementary operations is invariant under reindexing. -/
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)

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

@@ -97,7 +97,7 @@ def transvection (c : R) : Matrix n n R :=
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] (i : n) (j : n), Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) (Matrix.transvection.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (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_4)))))))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] (i : n) (j : n), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.transvection.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] (i : n) (j : n), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.transvection.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_zero Matrix.transvection_zeroₓ'. -/
 @[simp]
 theorem transvection_zero : transvection i j (0 : R) = 1 := by simp [transvection]
@@ -109,7 +109,7 @@ section
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] (i : n) (j : n) [_inst_5 : Finite.{succ u2} n] (c : R), Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_2 a b) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4))))))))) i (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (n -> R) (n -> R) (n -> R) (instHAdd.{max u2 u1} (n -> R) (Pi.instAdd.{u2, u1} n (fun (ᾰ : n) => R) (fun (i : n) => Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) i) (SMul.smul.{u1, max u2 u1} R (n -> R) (Function.hasSMul.{u2, u1, u1} n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))))) c (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) j)))) (Matrix.transvection.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j c)
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] (i : n) (j : n) [_inst_5 : Finite.{succ u1} n] (c : R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_2 a b) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) i (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (n -> R) (n -> R) (n -> R) (instHAdd.{max u2 u1} (n -> R) (Pi.instAdd.{u1, u2} n (fun (ᾰ : n) => R) (fun (i : n) => Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) i) (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (n -> R) (n -> R) (instHSMul.{u2, max u2 u1} R (n -> R) (Pi.instSMul.{u1, u2, u2} n R (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.12 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_4) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) c (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) j)))) (Matrix.transvection.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j c)
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] (i : n) (j : n) [_inst_5 : Finite.{succ u1} n] (c : R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_2 a b) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))))) i (HAdd.hAdd.{max u2 u1, max u2 u1, max u2 u1} (n -> R) (n -> R) (n -> R) (instHAdd.{max u2 u1} (n -> R) (Pi.instAdd.{u1, u2} n (fun (ᾰ : n) => R) (fun (i : n) => Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) i) (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (n -> R) (n -> R) (instHSMul.{u2, max u2 u1} R (n -> R) (Pi.instSMul.{u1, u2, u2} n R (fun (a._@.Mathlib.Data.Matrix.Basic._hyg.12 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) c (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) j)))) (Matrix.transvection.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j c)
 Case conversion may be inaccurate. Consider using '#align matrix.update_row_eq_transvection Matrix.updateRow_eq_transvectionₓ'. -/
 /-- A transvection matrix is obtained from the identity by adding `c` times the `j`-th row to
 the `i`-th row. -/
@@ -196,7 +196,7 @@ theorem mul_transvection_apply_of_ne (a b : n) (hb : b ≠ j) (c : R) (M : Matri
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] (i : n) (j : n) [_inst_5 : Fintype.{u2} n], (Ne.{succ u2} n i j) -> (forall (c : R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 R _inst_4 (Matrix.transvection.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j c)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] (i : n) (j : n) [_inst_5 : Fintype.{u1} n], (Ne.{succ u1} n i j) -> (forall (c : R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 R _inst_4 (Matrix.transvection.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j c)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] (i : n) (j : n) [_inst_5 : Fintype.{u1} n], (Ne.{succ u1} n i j) -> (forall (c : R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 R _inst_4 (Matrix.transvection.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 i j c)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_transvection_of_ne Matrix.det_transvection_of_neₓ'. -/
 @[simp]
 theorem det_transvection_of_ne (h : i ≠ j) (c : R) : det (transvection i j c) = 1 := by
@@ -255,7 +255,7 @@ theorem toMatrix_mk (i j : n) (hij : i ≠ j) (c : R) :
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] (t : Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 R _inst_4 (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 R _inst_4 (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 R _inst_4 (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.det Matrix.TransvectionStruct.detₓ'. -/
 @[simp]
 protected theorem det [Fintype n] (t : TransvectionStruct n R) : det t.toMatrix = 1 :=
@@ -266,7 +266,7 @@ protected theorem det [Fintype n] (t : TransvectionStruct n R) : det t.toMatrix
 lean 3 declaration is
   forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))), Eq.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L))) (OfNat.ofNat.{u2} 𝕜 1 (OfNat.mk.{u2} 𝕜 1 (One.one.{u2} 𝕜 (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))))))
 but is expected to have type
-  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)), Eq.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)), Eq.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.det_to_matrix_prod Matrix.TransvectionStruct.det_toMatrix_prodₓ'. -/
 @[simp]
 theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
@@ -301,7 +301,7 @@ variable [Fintype n]
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] (t : Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4), Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4 t)) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4 t)) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t)) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mulₓ'. -/
 theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 :=
   by
@@ -313,7 +313,7 @@ theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] (t : Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4), Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4 t))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (t : Matrix.TransvectionStruct.{u2, u1} n R), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4 t))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_invₓ'. -/
 theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 :=
   by
@@ -325,7 +325,7 @@ theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)), Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Function.comp.{succ (max u2 u1), max (succ u2) (succ u1), succ (max u2 u1)} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.inv.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)) (List.reverse.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R)), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Function.comp.{succ (max u1 u2), max (succ u1) (succ u2), succ (max u1 u2)} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4)) (List.reverse.{max u2 u1} (Matrix.TransvectionStruct.{u2, u1} n R) L))) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R)), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Function.comp.{succ (max u1 u2), max (succ u1) (succ u2), succ (max u1 u2)} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4)) (List.reverse.{max u2 u1} (Matrix.TransvectionStruct.{u2, u1} n R) L))) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.reverse_inv_prod_mul_prod Matrix.TransvectionStruct.reverse_inv_prod_mul_prodₓ'. -/
 theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
     (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod ⬝ (L.map toMatrix).Prod = 1 :=
@@ -344,7 +344,7 @@ theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
 lean 3 declaration is
   forall {n : Type.{u2}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)), Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Function.comp.{succ (max u2 u1), max (succ u2) (succ u1), succ (max u2 u1)} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.inv.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)) (List.reverse.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (OfNat.mk.{max u2 u1} (Matrix.{u2, u2, u1} n n R) 1 (One.one.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R)), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Function.comp.{succ (max u1 u2), max (succ u1) (succ u2), succ (max u1 u2)} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4)) (List.reverse.{max u2 u1} (Matrix.TransvectionStruct.{u2, u1} n R) L)))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))))
+  forall {n : Type.{u1}} {R : Type.{u2}} [_inst_2 : DecidableEq.{succ u1} n] [_inst_4 : CommRing.{u2} R] [_inst_5 : Fintype.{u1} n] (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R)), Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) (List.prod.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.instMulMatrix.{u2, u1} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))))) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Function.comp.{succ (max u1 u2), max (succ u1) (succ u2), succ (max u1 u2)} (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.TransvectionStruct.{u2, u1} n R) (Matrix.{u1, u1, u2} n n R) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.inv.{u2, u1} n R _inst_4)) (List.reverse.{max u2 u1} (Matrix.TransvectionStruct.{u2, u1} n R) L)))) (OfNat.ofNat.{max u2 u1} (Matrix.{u1, u1, u2} n n R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.one.{u2, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.prod_mul_reverse_inv_prod Matrix.TransvectionStruct.prod_mul_reverse_inv_prodₓ'. -/
 theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
     (L.map toMatrix).Prod ⬝ (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod = 1 :=
@@ -386,7 +386,7 @@ def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
 lean 3 declaration is
   forall {n : Type.{u2}} (p : Type.{u3}) {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] (t : Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4), Eq.{succ (max (max u2 u3) u1)} (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.TransvectionStruct.toMatrix.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => (fun (a : p) (b : p) => _inst_3 a b) a b) a b) _inst_4 (Matrix.TransvectionStruct.sumInl.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4 t)) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) (OfNat.ofNat.{max u3 u1} (Matrix.{u3, u3, u1} p p R) 1 (OfNat.mk.{max u3 u1} (Matrix.{u3, u3, u1} p p R) 1 (One.one.{max u3 u1} (Matrix.{u3, u3, u1} p p R) (Matrix.hasOne.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4))))))))))
 but is expected to have type
-  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] (t : Matrix.TransvectionStruct.{u3, u2} n R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u2 u1, max u2 u1, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u2 u1} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4 (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R t)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max u3 u1} (Matrix.{u1, u1, u3} p p R) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.one.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))))
+  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] (t : Matrix.TransvectionStruct.{u3, u2} n R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u2 u1, max u2 u1, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u2 u1} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4 (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R t)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max u3 u1} (Matrix.{u1, u1, u3} p p R) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.one.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_sum_inl Matrix.TransvectionStruct.toMatrix_sumInlₓ'. -/
 theorem toMatrix_sumInl (t : TransvectionStruct n R) :
     (t.sumInl p).toMatrix = fromBlocks t.toMatrix 0 0 1 :=
@@ -404,7 +404,7 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
 lean 3 declaration is
   forall {n : Type.{u2}} (p : Type.{u3}) {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u2, u2, u1} n n R) (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)) (N : Matrix.{u3, u3, u1} p p R), Eq.{succ (max (max u2 u3) u1)} (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.mul.{u1, max u2 u3, max u2 u3, max u2 u3} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R (Sum.fintype.{u2, u3} n p _inst_5 _inst_6) (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (List.prod.{max (max u2 u3) u1} (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.hasMul.{u1, max u2 u3} (Sum.{u2, u3} n p) R (Sum.fintype.{u2, u3} n p _inst_5 _inst_6) (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max (max u2 u3) u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Function.comp.{succ (max u2 u1), max (succ (max u2 u3)) (succ u1), succ (max (max u2 u3) u1)} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.TransvectionStruct.toMatrix.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4)) L)) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R M (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) N)) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) M) (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) N)
 but is expected to have type
-  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (M : Matrix.{u2, u2, u3} n n R) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)) (N : Matrix.{u1, u1, u3} p p R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u2 u1, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.mul.{u3, max u2 u1, max u2 u1, max u1 u2} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (List.prod.{max (max u3 u2) u1} (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.instMulMatrix.{u3, max u2 u1} (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, max u2 u1} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max (max u1 u2) u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Function.comp.{succ (max u2 u3), max (succ (max u1 u2)) (succ u3), succ (max (max u1 u2) u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, max u1 u2} (Sum.{u2, u1} n p) R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u1 u2} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R)) L)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R M (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R (Matrix.mul.{u3, u2, u2, u2} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) M) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)
+  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (M : Matrix.{u2, u2, u3} n n R) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)) (N : Matrix.{u1, u1, u3} p p R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u2 u1, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.mul.{u3, max u2 u1, max u2 u1, max u1 u2} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (List.prod.{max (max u3 u2) u1} (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.instMulMatrix.{u3, max u2 u1} (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, max u2 u1} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max (max u1 u2) u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Function.comp.{succ (max u2 u3), max (succ (max u1 u2)) (succ u3), succ (max (max u1 u2) u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, max u1 u2} (Sum.{u2, u1} n p) R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u1 u2} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R)) L)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R M (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R (Matrix.mul.{u3, u2, u2, u2} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) M) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mulₓ'. -/
 @[simp]
 theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
@@ -421,7 +421,7 @@ theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
 lean 3 declaration is
   forall {n : Type.{u2}} (p : Type.{u3}) {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u2, u2, u1} n n R) (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)) (N : Matrix.{u3, u3, u1} p p R), Eq.{succ (max (max u2 u3) u1)} (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.mul.{u1, max u2 u3, max u2 u3, max u2 u3} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R (Sum.fintype.{u2, u3} n p _inst_5 _inst_6) (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R M (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) N) (List.prod.{max (max u2 u3) u1} (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.hasMul.{u1, max u2 u3} (Sum.{u2, u3} n p) R (Sum.fintype.{u2, u3} n p _inst_5 _inst_6) (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max (max u2 u3) u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Function.comp.{succ (max u2 u1), max (succ (max u2 u3)) (succ u1), succ (max (max u2 u3) u1)} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.TransvectionStruct.toMatrix.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4)) L))) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) M (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) N)
 but is expected to have type
-  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (M : Matrix.{u2, u2, u3} n n R) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)) (N : Matrix.{u1, u1, u3} p p R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u1 u2, max u2 u1, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.mul.{u3, max u1 u2, max u1 u2, max u2 u1} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R M (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N) (List.prod.{max (max u3 u2) u1} (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.instMulMatrix.{u3, max u2 u1} (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, max u2 u1} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max (max u1 u2) u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Function.comp.{succ (max u2 u3), max (succ (max u1 u2)) (succ u3), succ (max (max u1 u2) u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, max u1 u2} (Sum.{u2, u1} n p) R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u1 u2} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R)) L))) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R (Matrix.mul.{u3, u2, u2, u2} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) M (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)
+  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (M : Matrix.{u2, u2, u3} n n R) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)) (N : Matrix.{u1, u1, u3} p p R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u1 u2, max u2 u1, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.mul.{u3, max u1 u2, max u1 u2, max u2 u1} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R M (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N) (List.prod.{max (max u3 u2) u1} (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.instMulMatrix.{u3, max u2 u1} (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, max u2 u1} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max (max u1 u2) u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Function.comp.{succ (max u2 u3), max (succ (max u1 u2)) (succ u3), succ (max (max u1 u2) u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, max u1 u2} (Sum.{u2, u1} n p) R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u1 u2} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R)) L))) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R (Matrix.mul.{u3, u2, u2, u2} n n n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) M (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.mul_sum_inl_to_matrix_prod Matrix.TransvectionStruct.mul_sumInl_toMatrix_prodₓ'. -/
 @[simp]
 theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
@@ -475,7 +475,7 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
 lean 3 declaration is
   forall {n : Type.{u2}} {p : Type.{u3}} {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u3} p] (e : Equiv.{succ u2, succ u3} n p) (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)), Eq.{succ (max u3 u1)} (Matrix.{u3, u3, u1} p p R) (List.prod.{max u3 u1} (Matrix.{u3, u3, u1} p p R) (Matrix.hasMul.{u1, u3} p R _inst_6 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u3 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u3, u3, u1} p p R) (Function.comp.{succ (max u2 u1), max (succ u3) (succ u1), succ (max u3 u1)} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.TransvectionStruct.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4) (Matrix.{u3, u3, u1} p p R) (Matrix.TransvectionStruct.toMatrix.{u1, u3} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4) (Matrix.TransvectionStruct.reindexEquiv.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4 e)) L)) (coeFn.{max (succ (max u2 u1)) (succ (max u3 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (AlgEquiv.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (fun (_x : AlgEquiv.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) => (Matrix.{u2, u2, u1} n n R) -> (Matrix.{u3, u3, u1} p p R)) (AlgEquiv.hasCoeToFun.{u1, max u2 u1, max u3 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.{u3, u3, u1} p p R) (CommRing.toCommSemiring.{u1} R _inst_4) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u1, u3} p R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (Matrix.algebra.{u1, u3, u1} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u1} R _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (Matrix.reindexAlgEquiv.{u2, u3, u1} n p R (CommRing.toCommSemiring.{u1} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
 but is expected to have type
-  forall {n : Type.{u2}} {p : Type.{u1}} {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (e : Equiv.{succ u2, succ u1} n p) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)), Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} p p R) (List.prod.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.instMulMatrix.{u3, u1} p R _inst_6 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max u1 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u1, u1, u3} p p R) (Function.comp.{succ (max u2 u3), max (succ u1) (succ u3), succ (max u1 u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, u1} p R) (Matrix.{u1, u1, u3} p p R) (Matrix.TransvectionStruct.toMatrix.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) _inst_4) (Matrix.TransvectionStruct.reindexEquiv.{u3, u2, u1} n p R e)) L)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u3) (succ u2), max (succ u3) (succ u1)} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (Matrix.{u2, u2, u3} n n R) (fun (_x : Matrix.{u2, u2, u3} n n R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u3} n n R) => Matrix.{u1, u1, u3} p p R) _x) (SMulHomClass.toFunLike.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (SMulZeroClass.toSMul.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (AddMonoid.toZero.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (SMulZeroClass.toSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) 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(Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) 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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
+  forall {n : Type.{u2}} {p : Type.{u1}} {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (e : Equiv.{succ u2, succ u1} n p) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)), Eq.{max (succ u3) (succ u1)} (Matrix.{u1, u1, u3} p p R) (List.prod.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.instMulMatrix.{u3, u1} p R _inst_6 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u1} p R (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R 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u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Semiring.toOne.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
 Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv_prod Matrix.TransvectionStruct.toMatrix_reindexEquiv_prodₓ'. -/
 theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n R)) :
     (L.map (toMatrix ∘ reindexEquiv e)).Prod = reindexAlgEquiv R e (L.map toMatrix).Prod :=
@@ -535,7 +535,7 @@ def listTransvecRow : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.drop.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M))) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat instLENat k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.drop.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M))) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat instLENat k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.drop.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M))) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_row_drop Matrix.Pivot.listTransvecCol_mul_last_row_dropₓ'. -/
 /-- Multiplying by some of the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
@@ -555,7 +555,7 @@ theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i)
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i)
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_row Matrix.Pivot.listTransvecCol_mul_last_rowₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row (i : Sum (Fin r) Unit) :
@@ -567,7 +567,7 @@ theorem listTransvecCol_mul_last_row (i : Sum (Fin r) Unit) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_col Matrix.Pivot.listTransvecCol_mul_last_colₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_col M` kills all the coefficients in the
 last column but the last one. -/
@@ -619,7 +619,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.take.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat instLENat k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.take.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat instLENat k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.take.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_takeₓ'. -/
 /-- Multiplying by some of the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
@@ -646,7 +646,7 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_col Matrix.Pivot.mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
@@ -661,7 +661,7 @@ theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_row M` kills all the coefficients in the
 last row but the last one. -/
@@ -716,7 +716,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last row but the last one. -/
@@ -735,7 +735,7 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last column but the last one. -/
@@ -754,7 +754,7 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` turns
 the matrix in block-diagonal form. -/
@@ -775,7 +775,7 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) (fun (L : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) => Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) (fun (L' : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) => Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) (fun (L : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) => Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) (fun (L' : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) => Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) (fun (L : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) => Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) (fun (L' : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) => Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zeroₓ'. -/
 /-- There exist two lists of `transvection_struct` such that multiplying by them on the left and
 on the right makes a matrix block-diagonal, when the last coefficient is nonzero. -/
@@ -887,7 +887,7 @@ variable {n p} [Fintype n] [Fintype p]
 lean 3 declaration is
   forall {n : Type.{u1}} {p : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : Field.{u3} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u2} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u2} p] (M : Matrix.{u2, u2, u3} p p 𝕜) (e : Equiv.{succ u2, succ u1} p n), (Exists.{succ (max u1 u3)} (List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L : List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{succ (max u1 u3)} (List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u3)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u3)} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.mul.{u3, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))))) (Matrix.mul.{u3, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))))) (List.prod.{max u1 u3} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.hasMul.{u3, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u3} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u3} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u3} 𝕜 (Ring.toAddCommGroupWithOne.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (List.map.{max u1 u3, max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) L)) (coeFn.{max (succ (max u2 u3)) (succ (max u1 u3)), max (succ (max u2 u3)) (succ (max u1 u3))} (AlgEquiv.{u3, max u2 u3, max u1 u3} 𝕜 (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.{u1, u1, u3} n n 𝕜) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (Matrix.semiring.{u3, u2} p 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u3, u1} n 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u3, u2, u3} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)))) (Matrix.algebra.{u3, u1, u3} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))))) (fun (_x : AlgEquiv.{u3, max u2 u3, max u1 u3} 𝕜 (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.{u1, u1, u3} n n 𝕜) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (Matrix.semiring.{u3, u2} p 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u3, u1} n 𝕜 (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u3, u2, u3} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)))) (Matrix.algebra.{u3, u1, u3} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))))) => (Matrix.{u2, u2, u3} p p 𝕜) -> (Matrix.{u1, u1, u3} n n 𝕜)) (AlgEquiv.hasCoeToFun.{u3, max u2 u3, max u1 u3} 𝕜 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𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))) (Algebra.id.{u3} 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} p n 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u3} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.hasMul.{u3, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 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(NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) D))))) -> (Exists.{succ (max u2 u3)} (List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{succ (max u2 u3)} (List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L' : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{max 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(Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u3} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u3} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u3} 𝕜 (Ring.toAddCommGroupWithOne.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) L)) M) (List.prod.{max u2 u3} (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.hasMul.{u3, u2} p 𝕜 _inst_6 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (Matrix.hasOne.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u3} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u3} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u3} 𝕜 (Ring.toAddCommGroupWithOne.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) (Matrix.{u2, u2, u3} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u3, u2} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (MulZeroClass.toHasZero.{u3} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) D)))))
 but is expected to have type
-  forall {n : Type.{u1}} {p : Type.{u3}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u3, u3, u2} p p 𝕜) (e : Equiv.{succ u3, succ u1} p n), (Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Matrix.{u3, u3, u2} p p 𝕜) (fun (_x : Matrix.{u3, u3, u2} p p 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u3, u3, u2} p p 𝕜) => Matrix.{u1, u1, u2} n n 𝕜) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (SMulZeroClass.toSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toZero.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u1 u3) u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AlgEquivClass.toAlgHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, max u1 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))))))) (Matrix.reindexAlgEquiv.{u3, u1, u2} p n 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) 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_inst_1))) L)) M) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) 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+  forall {n : Type.{u1}} {p : Type.{u3}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u3, u3, u2} p p 𝕜) (e : Equiv.{succ u3, succ u1} p n), (Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 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(Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (SMulZeroClass.toSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toZero.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u1 u3) u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AlgEquivClass.toAlgHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, max u1 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))))))) (Matrix.reindexAlgEquiv.{u3, u1, u2} p n 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D))))) -> (Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L' : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (p -> 𝕜) (fun (D : p -> 𝕜) => Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.mul.{u2, u3, u3, u3} p p p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u3, u3, u3} p p p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toOne.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D)))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Reduction to diagonal form by elementary operations is invariant under reindexing. -/
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)
@@ -942,7 +942,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
 lean 3 declaration is
   forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (M : Matrix.{u1, u1, u2} n n 𝕜), Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D))))
 but is expected to have type
-  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n 𝕜), Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L' : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D))))
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n 𝕜), Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L' : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
@@ -958,7 +958,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
 lean 3 declaration is
   forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (M : Matrix.{u1, u1, u2} n n 𝕜), Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n 𝕜) M (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))))))
 but is expected to have type
-  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n 𝕜), Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L' : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n 𝕜) M (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D)) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n 𝕜), Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L' : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n 𝕜) M (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D)) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
 Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvecₓ'. -/
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
 transvections.-/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.transvection
-! leanprover-community/mathlib commit 0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Tactic.FieldSimp
 /-!
 # Transvections
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Transvections are matrices of the form `1 + std_basis_matrix i j c`, where `std_basis_matrix i j c`
 is the basic matrix with a `c` at position `(i, j)`. Multiplying by such a transvection on the left
 (resp. on the right) amounts to adding `c` times the `j`-th row to to the `i`-th row

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

@@ -80,6 +80,7 @@ section Transvection
 
 variable {R n} (i j : n)
 
+#print Matrix.transvection /-
 /-- The transvection matrix `transvection i j c` is equal to the identity plus `c` at position
 `(i, j)`. Multiplying by it on the left (as in `transvection i j c ⬝ M`) corresponds to adding
 `c` times the `j`-th line of `M` to its `i`-th line. Multiplying by it on the right corresponds
@@ -87,13 +88,26 @@ to adding `c` times the `i`-th column to the `j`-th column. -/
 def transvection (c : R) : Matrix n n R :=
   1 + Matrix.stdBasisMatrix i j c
 #align matrix.transvection Matrix.transvection
+-/
 
+/- warning: matrix.transvection_zero -> Matrix.transvection_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_zero Matrix.transvection_zeroₓ'. -/
 @[simp]
 theorem transvection_zero : transvection i j (0 : R) = 1 := by simp [transvection]
 #align matrix.transvection_zero Matrix.transvection_zero
 
 section
 
+/- warning: matrix.update_row_eq_transvection -> Matrix.updateRow_eq_transvection is a dubious translation:
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 /-- A transvection matrix is obtained from the identity by adding `c` times the `j`-th row to
 the `i`-th row. -/
 theorem updateRow_eq_transvection [Finite n] (c : R) :
@@ -118,33 +132,69 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
 
 variable [Fintype n]
 
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 theorem transvection_mul_transvection_same (h : i ≠ j) (c d : R) :
     transvection i j c ⬝ transvection i j d = transvection i j (c + d) := by
   simp [transvection, Matrix.add_mul, Matrix.mul_add, h, h.symm, add_smul, add_assoc,
     std_basis_matrix_add]
 #align matrix.transvection_mul_transvection_same Matrix.transvection_mul_transvection_same
 
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 @[simp]
 theorem transvection_mul_apply_same (b : n) (c : R) (M : Matrix n n R) :
     (transvection i j c ⬝ M) i b = M i b + c * M j b := by simp [transvection, Matrix.add_mul]
 #align matrix.transvection_mul_apply_same Matrix.transvection_mul_apply_same
 
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_transvection_apply_same Matrix.mul_transvection_apply_sameₓ'. -/
 @[simp]
 theorem mul_transvection_apply_same (a : n) (c : R) (M : Matrix n n R) :
     (M ⬝ transvection i j c) a j = M a j + c * M a i := by
   simp [transvection, Matrix.mul_add, mul_comm]
 #align matrix.mul_transvection_apply_same Matrix.mul_transvection_apply_same
 
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_mul_apply_of_ne Matrix.transvection_mul_apply_of_neₓ'. -/
 @[simp]
 theorem transvection_mul_apply_of_ne (a b : n) (ha : a ≠ i) (c : R) (M : Matrix n n R) :
     (transvection i j c ⬝ M) a b = M a b := by simp [transvection, Matrix.add_mul, ha]
 #align matrix.transvection_mul_apply_of_ne Matrix.transvection_mul_apply_of_ne
 
+/- warning: matrix.mul_transvection_apply_of_ne -> Matrix.mul_transvection_apply_of_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.mul_transvection_apply_of_ne Matrix.mul_transvection_apply_of_neₓ'. -/
 @[simp]
 theorem mul_transvection_apply_of_ne (a b : n) (hb : b ≠ j) (c : R) (M : Matrix n n R) :
     (M ⬝ transvection i j c) a b = M a b := by simp [transvection, Matrix.mul_add, hb]
 #align matrix.mul_transvection_apply_of_ne Matrix.mul_transvection_apply_of_ne
 
+/- warning: matrix.det_transvection_of_ne -> Matrix.det_transvection_of_ne 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.det_transvection_of_ne Matrix.det_transvection_of_neₓ'. -/
 @[simp]
 theorem det_transvection_of_ne (h : i ≠ j) (c : R) : det (transvection i j c) = 1 := by
   rw [← update_row_eq_transvection i j, det_update_row_add_smul_self _ h, det_one]
@@ -154,6 +204,12 @@ end
 
 variable (R n)
 
+/- warning: matrix.transvection_struct -> Matrix.TransvectionStruct is a dubious translation:
+lean 3 declaration is
+  forall (n : Type.{u2}) (R : Type.{u1}) [_inst_2 : DecidableEq.{succ u2} n] [_inst_4 : CommRing.{u1} R], Sort.{max (succ u2) (succ u1)}
+but is expected to have type
+  Type.{u2} -> Type.{u1} -> Sort.{max (succ u2) (succ u1)}
+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct Matrix.TransvectionStructₓ'. -/
 /-- A structure containing all the information from which one can build a nontrivial transvection.
 This structure is easier to manipulate than transvections as one has a direct access to all the
 relevant fields. -/
@@ -173,22 +229,42 @@ namespace TransvectionStruct
 
 variable {R n}
 
+#print Matrix.TransvectionStruct.toMatrix /-
 /-- Associating to a `transvection_struct` the corresponding transvection matrix. -/
 def toMatrix (t : TransvectionStruct n R) : Matrix n n R :=
   transvection t.i t.j t.c
 #align matrix.transvection_struct.to_matrix Matrix.TransvectionStruct.toMatrix
+-/
 
+/- warning: matrix.transvection_struct.to_matrix_mk -> Matrix.TransvectionStruct.toMatrix_mk is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_mk Matrix.TransvectionStruct.toMatrix_mkₓ'. -/
 @[simp]
 theorem toMatrix_mk (i j : n) (hij : i ≠ j) (c : R) :
     TransvectionStruct.toMatrix ⟨i, j, hij, c⟩ = transvection i j c :=
   rfl
 #align matrix.transvection_struct.to_matrix_mk Matrix.TransvectionStruct.toMatrix_mk
 
+/- warning: matrix.transvection_struct.det -> Matrix.TransvectionStruct.det is a dubious translation:
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 @[simp]
 protected theorem det [Fintype n] (t : TransvectionStruct n R) : det t.toMatrix = 1 :=
   det_transvection_of_ne _ _ t.hij _
 #align matrix.transvection_struct.det Matrix.TransvectionStruct.det
 
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 @[simp]
 theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
     det (L.map toMatrix).Prod = 1 := by
@@ -197,6 +273,12 @@ theorem det_toMatrix_prod [Fintype n] (L : List (TransvectionStruct n 𝕜)) :
   · simp [IH]
 #align matrix.transvection_struct.det_to_matrix_prod Matrix.TransvectionStruct.det_toMatrix_prod
 
+/- warning: matrix.transvection_struct.inv -> Matrix.TransvectionStruct.inv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.inv Matrix.TransvectionStruct.invₓ'. -/
 /-- The inverse of a `transvection_struct`, designed so that `t.inv.to_matrix` is the inverse of
 `t.to_matrix`. -/
 @[simps]
@@ -212,18 +294,36 @@ section
 
 variable [Fintype n]
 
+/- warning: matrix.transvection_struct.inv_mul -> Matrix.TransvectionStruct.inv_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mulₓ'. -/
 theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 :=
   by
   rcases t with ⟨⟩
   simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mul
 
+/- warning: matrix.transvection_struct.mul_inv -> Matrix.TransvectionStruct.mul_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_invₓ'. -/
 theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 :=
   by
   rcases t with ⟨⟩
   simp [to_matrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_inv
 
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.reverse_inv_prod_mul_prod Matrix.TransvectionStruct.reverse_inv_prod_mul_prodₓ'. -/
 theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
     (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod ⬝ (L.map toMatrix).Prod = 1 :=
   by
@@ -237,6 +337,12 @@ theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
     simpa [inv_mul] using IH
 #align matrix.transvection_struct.reverse_inv_prod_mul_prod Matrix.TransvectionStruct.reverse_inv_prod_mul_prod
 
+/- warning: matrix.transvection_struct.prod_mul_reverse_inv_prod -> Matrix.TransvectionStruct.prod_mul_reverse_inv_prod is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.prod_mul_reverse_inv_prod Matrix.TransvectionStruct.prod_mul_reverse_inv_prodₓ'. -/
 theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
     (L.map toMatrix).Prod ⬝ (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).Prod = 1 :=
   by
@@ -257,6 +363,12 @@ variable (p)
 
 open Sum
 
+/- warning: matrix.transvection_struct.sum_inl -> Matrix.TransvectionStruct.sumInl is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u2}} (p : Type.{u3}) {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R], (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) -> (Matrix.TransvectionStruct.{u1, max u2 u3} (Sum.{u2, u3} n p) R (fun (a : Sum.{u2, u3} n p) (b : Sum.{u2, u3} n p) => Sum.decidableEq.{u2, u3} n (fun (a : n) (b : n) => _inst_2 a b) p (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4)
+but is expected to have type
+  forall {n : Type.{u2}} (p : Type.{u3}) {R : Type.{u1}}, (Matrix.TransvectionStruct.{u1, u2} n R) -> (Matrix.TransvectionStruct.{u1, max u3 u2} (Sum.{u2, u3} n p) R)
+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.sum_inl Matrix.TransvectionStruct.sumInlₓ'. -/
 /-- Given a `transvection_struct` on `n`, define the corresponding `transvection_struct` on `n ⊕ p`
 using the identity on `p`. -/
 def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
@@ -267,6 +379,12 @@ def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R
   c := t.c
 #align matrix.transvection_struct.sum_inl Matrix.TransvectionStruct.sumInl
 
+/- warning: matrix.transvection_struct.to_matrix_sum_inl -> Matrix.TransvectionStruct.toMatrix_sumInl is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_sum_inl Matrix.TransvectionStruct.toMatrix_sumInlₓ'. -/
 theorem toMatrix_sumInl (t : TransvectionStruct n R) :
     (t.sumInl p).toMatrix = fromBlocks t.toMatrix 0 0 1 :=
   by
@@ -279,6 +397,12 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
   · by_cases h : a = b <;> simp [transvection_struct.sum_inl, transvection, h]
 #align matrix.transvection_struct.to_matrix_sum_inl Matrix.TransvectionStruct.toMatrix_sumInl
 
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b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u1, u2, u3} n p R (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) _inst_4)) L)) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R M (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) N)) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasMul.{u1, u2} n R _inst_5 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (Matrix.hasOne.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 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_4)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) (Matrix.{u2, u2, u1} n n R) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) M) (OfNat.ofNat.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (OfNat.mk.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) 0 (Zero.zero.{max u2 u3 u1} (Matrix.{u2, u3, u1} n p R) (Matrix.hasZero.{u1, u2, u3} n p R (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_4)))))))))) (OfNat.ofNat.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (OfNat.mk.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) 0 (Zero.zero.{max u3 u2 u1} (Matrix.{u3, u2, u1} p n R) (Matrix.hasZero.{u1, u3, u2} p n R (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_4)))))))))) N)
+but is expected to have type
+  forall {n : Type.{u2}} (p : Type.{u1}) {R : Type.{u3}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u1} p] [_inst_4 : CommRing.{u3} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u1} p] (M : Matrix.{u2, u2, u3} n n R) (L : List.{max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R)) (N : Matrix.{u1, u1, u3} p p R), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (Matrix.{max u2 u1, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.mul.{u3, max u2 u1, max u2 u1, max u1 u2} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R (instFintypeSum.{u2, u1} n p _inst_5 _inst_6) (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4))))) (List.prod.{max (max 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u2 u3, max (max u1 u2) u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Function.comp.{succ (max u2 u3), max (succ (max u1 u2)) (succ u3), succ (max (max u1 u2) u3)} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.TransvectionStruct.{u3, max u1 u2} (Sum.{u2, u1} n p) R) (Matrix.{max u1 u2, max u1 u2, u3} (Sum.{u2, u1} n p) (Sum.{u2, u1} n p) R) (Matrix.TransvectionStruct.toMatrix.{u3, max u1 u2} (Sum.{u2, u1} n p) R (fun (a : Sum.{u2, u1} n p) (b : Sum.{u2, u1} n p) => Sum.instDecidableEqSum.{u2, u1} n p (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) a b) _inst_4) (Matrix.TransvectionStruct.sumInl.{u3, u2, u1} n p R)) L)) (Matrix.fromBlocks.{u2, u1, u2, u1, u3} n p n p R M (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R 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(NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)) M) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u2, u1, u3} n p R) (Matrix.zero.{u3, u2, u1} n p R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) (OfNat.ofNat.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) 0 (Zero.toOfNat0.{max (max u3 u2) u1} (Matrix.{u1, u2, u3} p n R) (Matrix.zero.{u3, u1, u2} p n R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))) N)
+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mulₓ'. -/
 @[simp]
 theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
@@ -290,6 +414,12 @@ theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
   · simp [Matrix.mul_assoc, IH, to_matrix_sum_inl, from_blocks_multiply]
 #align matrix.transvection_struct.sum_inl_to_matrix_prod_mul Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul
 
+/- warning: matrix.transvection_struct.mul_sum_inl_to_matrix_prod -> Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u2}} (p : Type.{u3}) {R : Type.{u1}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_4 : CommRing.{u1} R] [_inst_5 : Fintype.{u2} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u2, u2, u1} n n R) (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4)) (N : Matrix.{u3, u3, u1} p p R), Eq.{succ (max (max u2 u3) u1)} (Matrix.{max u2 u3, max u2 u3, u1} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R) (Matrix.mul.{u1, max u2 u3, max u2 u3, max u2 u3} (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) (Sum.{u2, u3} n p) R (Sum.fintype.{u2, u3} n p _inst_5 _inst_6) (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Matrix.fromBlocks.{u2, u3, u2, u3, u1} n p n p R M (OfNat.ofNat.{max u2 u3 u1} 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.mul_sum_inl_to_matrix_prod Matrix.TransvectionStruct.mul_sumInl_toMatrix_prodₓ'. -/
 @[simp]
 theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
@@ -303,6 +433,12 @@ theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
 
 variable {p}
 
+/- warning: matrix.transvection_struct.reindex_equiv -> Matrix.TransvectionStruct.reindexEquiv is a dubious translation:
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+but is expected to have type
+  forall {n : Type.{u2}} {p : Type.{u3}} {R : Type.{u1}}, (Equiv.{succ u2, succ u3} n p) -> (Matrix.TransvectionStruct.{u1, u2} n R) -> (Matrix.TransvectionStruct.{u1, u3} p R)
+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.reindex_equiv Matrix.TransvectionStruct.reindexEquivₓ'. -/
 /-- Given a `transvection_struct` on `n` and an equivalence between `n` and `p`, define the
 corresponding `transvection_struct` on `p`. -/
 def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct p R
@@ -315,6 +451,12 @@ def reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) : TransvectionStruct
 
 variable [Fintype n] [Fintype p]
 
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(CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) 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(CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 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_inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4 t))
+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquivₓ'. -/
 theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix :=
   by
@@ -326,6 +468,12 @@ theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     simp [ha, hb, hab, ← e.apply_eq_iff_eq_symm_apply, std_basis_matrix]
 #align matrix.transvection_struct.to_matrix_reindex_equiv Matrix.TransvectionStruct.toMatrix_reindexEquiv
 
+/- warning: matrix.transvection_struct.to_matrix_reindex_equiv_prod -> Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod is a dubious translation:
+lean 3 declaration is
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u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (Module.toDistribMulAction.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u3, max u3 u2} R (Matrix.{u2, u2, u3} n n R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (Module.toDistribMulAction.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} p p R) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u3, max u3 u1} R (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, max u3 u2, max u3 u1, max (max u3 u2) u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) (AlgEquivClass.toAlgHomClass.{max (max u3 u2) u1, u3, max u3 u2, max u3 u1} (AlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)))) R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, max u3 u2, max u3 u1} R (Matrix.{u2, u2, u3} n n R) (Matrix.{u1, u1, u3} p p R) (CommRing.toCommSemiring.{u3} R _inst_4) (Matrix.semiring.{u3, u2} n R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.semiring.{u3, u1} p R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u2, u3} n R R _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u3} p R R _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (CommRing.toCommSemiring.{u3} R _inst_4) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))))))))) (Matrix.reindexAlgEquiv.{u2, u1, u3} n p R (CommRing.toCommSemiring.{u3} R _inst_4) _inst_6 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (fun (a : p) (b : p) => _inst_3 a b) e) (List.prod.{max u3 u2} (Matrix.{u2, u2, u3} n n R) (Matrix.instMulMatrix.{u3, u2} n R _inst_5 (NonUnitalNonAssocRing.toMul.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} R (NonAssocRing.toNonUnitalNonAssocRing.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))))) (Matrix.one.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_4))) (NonAssocRing.toOne.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_4)))) (List.map.{max u2 u3, max u2 u3} (Matrix.TransvectionStruct.{u3, u2} n R) (Matrix.{u2, u2, u3} n n R) (Matrix.TransvectionStruct.toMatrix.{u3, u2} n R (fun (a : n) (b : n) => _inst_2 a b) _inst_4) L)))
+Case conversion may be inaccurate. Consider using '#align matrix.transvection_struct.to_matrix_reindex_equiv_prod Matrix.TransvectionStruct.toMatrix_reindexEquiv_prodₓ'. -/
 theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n R)) :
     (L.map (toMatrix ∘ reindexEquiv e)).Prod = reindexAlgEquiv R e (L.map toMatrix).Prod :=
   by
@@ -362,20 +510,30 @@ variable {R} {r : ℕ} (M : Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜)
 
 open Sum Unit Fin TransvectionStruct
 
+#print Matrix.Pivot.listTransvecCol /-
 /-- A list of transvections such that multiplying on the left with these transvections will replace
 the last column with zeroes. -/
 def listTransvecCol : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :=
   List.ofFn fun i : Fin r =>
     transvection (inl i) (inr unit) <| -M (inl i) (inr unit) / M (inr unit) (inr unit)
 #align matrix.pivot.list_transvec_col Matrix.Pivot.listTransvecCol
+-/
 
+#print Matrix.Pivot.listTransvecRow /-
 /-- A list of transvections such that multiplying on the right with these transvections will replace
 the last row with zeroes. -/
 def listTransvecRow : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :=
   List.ofFn fun i : Fin r =>
     transvection (inr unit) (inl i) <| -M (inr unit) (inl i) / M (inr unit) (inr unit)
 #align matrix.pivot.list_transvec_row Matrix.Pivot.listTransvecRow
+-/
 
+/- warning: matrix.pivot.list_transvec_col_mul_last_row_drop -> Matrix.Pivot.listTransvecCol_mul_last_row_drop is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.drop.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M))) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat instLENat k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.drop.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M))) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_row_drop Matrix.Pivot.listTransvecCol_mul_last_row_dropₓ'. -/
 /-- Multiplying by some of the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (((listTransvecCol M).drop k).Prod ⬝ M) (inr unit) i = M (inr unit) i :=
@@ -390,12 +548,24 @@ theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     simpa [list_transvec_col, Matrix.mul_assoc]
 #align matrix.pivot.list_transvec_col_mul_last_row_drop Matrix.Pivot.listTransvecCol_mul_last_row_drop
 
+/- warning: matrix.pivot.list_transvec_col_mul_last_row -> Matrix.Pivot.listTransvecCol_mul_last_row is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i) (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) i)
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_row Matrix.Pivot.listTransvecCol_mul_last_rowₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_col M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row (i : Sum (Fin r) Unit) :
     ((listTransvecCol M).Prod ⬝ M) (inr unit) i = M (inr unit) i := by
   simpa using list_transvec_col_mul_last_row_drop M i (zero_le _)
 #align matrix.pivot.list_transvec_col_mul_last_row Matrix.Pivot.listTransvecCol_mul_last_row
 
+/- warning: matrix.pivot.list_transvec_col_mul_last_col -> Matrix.Pivot.listTransvecCol_mul_last_col is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_last_col Matrix.Pivot.listTransvecCol_mul_last_colₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_col M` kills all the coefficients in the
 last column but the last one. -/
 theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
@@ -442,6 +612,12 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         · simpa only [not_le] using hi
 #align matrix.pivot.list_transvec_col_mul_last_col Matrix.Pivot.listTransvecCol_mul_last_col
 
+/- warning: matrix.pivot.mul_list_transvec_row_last_col_take -> Matrix.Pivot.mul_listTransvecRow_last_col_take is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat Nat.hasLe k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.take.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit) {k : Nat}, (LE.le.{0} Nat instLENat k r) -> (Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.take.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) k (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_takeₓ'. -/
 /-- Multiplying by some of the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (M ⬝ ((listTransvecRow M).take k).Prod) i (inr unit) = M i (inr unit) :=
@@ -463,6 +639,12 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     simp only [Ne.def, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
 
+/- warning: matrix.pivot.mul_list_transvec_row_last_col -> Matrix.Pivot.mul_listTransvecRow_last_col is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (i : Sum.{0, 0} (Fin r) Unit), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (M i (Sum.inr.{0, 0} (Fin r) Unit Unit.unit))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_col Matrix.Pivot.mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_row M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
     (M ⬝ (listTransvecRow M).Prod) i (inr unit) = M i (inr unit) :=
@@ -472,6 +654,12 @@ theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
   simpa using mul_list_transvec_row_last_col_take M i le_rfl
 #align matrix.pivot.mul_list_transvec_row_last_col Matrix.Pivot.mul_listTransvecRow_last_col
 
+/- warning: matrix.pivot.mul_list_transvec_row_last_row -> Matrix.Pivot.mul_listTransvecRow_last_row is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) M (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices in `list_transvec_row M` kills all the coefficients in the
 last row but the last one. -/
 theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
@@ -521,6 +709,12 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         · simpa only [hni.symm, not_le, or_false_iff] using Nat.lt_succ_iff_lt_or_eq.1 hi
 #align matrix.pivot.mul_list_transvec_row_last_row Matrix.Pivot.mul_listTransvecRow_last_row
 
+/- warning: matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col -> Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inl.{0, 0} (Fin r) Unit i)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_colₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last row but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr unit) ≠ 0)
@@ -534,6 +728,12 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr
   simpa [list_transvec_col_mul_last_row] using hM
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_col Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col
 
+/- warning: matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row -> Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (i : Fin r), Eq.{succ u1} 𝕜 (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M)) (Sum.inl.{0, 0} (Fin r) Unit i) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_rowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` kills
 all the coefficients in the last column but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0)
@@ -547,6 +747,12 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr
   simpa [mul_list_transvec_row_last_col] using hM
 #align matrix.pivot.list_transvec_col_mul_mul_list_transvec_row_last_row Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row
 
+/- warning: matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row -> Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecCol.{u1} 𝕜 _inst_1 r M)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (Matrix.Pivot.listTransvecRow.{u1} 𝕜 _inst_1 r M))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRowₓ'. -/
 /-- Multiplying by all the matrices either in `list_transvec_col M` and `list_transvec_row M` turns
 the matrix in block-diagonal form. -/
 theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
@@ -562,6 +768,12 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
     simp [to_blocks₂₁, this, list_transvec_col_mul_mul_list_transvec_row_last_col M hM]
 #align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
 
+/- warning: matrix.pivot.exists_is_two_block_diagonal_of_ne_zero -> Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))))))) -> (Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) (fun (L : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) => Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) (fun (L' : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)))) => Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.hasMul.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (Sum.fintype.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.hasOne.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.decidableEq.{0, 0} (Fin r) (fun (a : Fin r) (b : Fin r) => Fin.decidableEq r a b) Unit (fun (a : Unit) (b : Unit) => PUnit.decidableEq.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] {r : Nat} (M : Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜), (Ne.{succ u1} 𝕜 (M (Sum.inr.{0, 0} (Fin r) Unit Unit.unit) (Sum.inr.{0, 0} (Fin r) Unit Unit.unit)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) (fun (L : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) => Exists.{succ u1} (List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) (fun (L' : List.{u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜)) => Matrix.IsTwoBlockDiagonal.{0, 0, 0, 0, u1} (Fin r) Unit (Fin r) Unit 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, 0, 0, 0} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{u1} (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.instMulMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (instFintypeSum.{0, 0} (Fin r) Unit (Fin.fintype r) PUnit.fintype.{0}) (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{u1, u1} (Matrix.TransvectionStruct.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.{0, 0, u1} (Sum.{0, 0} (Fin r) Unit) (Sum.{0, 0} (Fin r) Unit) 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, 0} (Sum.{0, 0} (Fin r) Unit) 𝕜 (fun (a : Sum.{0, 0} (Fin r) Unit) (b : Sum.{0, 0} (Fin r) Unit) => Sum.instDecidableEqSum.{0, 0} (Fin r) Unit (fun (a : Fin r) (b : Fin r) => instDecidableEqFin r a b) (fun (a : Unit) (b : Unit) => instDecidableEqPUnit.{1} a b) a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zeroₓ'. -/
 /-- There exist two lists of `transvection_struct` such that multiplying by them on the left and
 on the right makes a matrix block-diagonal, when the last coefficient is nonzero. -/
 theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0) :
@@ -582,6 +794,7 @@ theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0
 #align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec /-
 /-- There exist two lists of `transvection_struct` such that multiplying by them on the left and
 on the right makes a matrix block-diagonal. -/
 theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
@@ -625,7 +838,9 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
     rw [Matrix.mul_assoc (L.map to_matrix).Prod]
     exact hLL'
 #align matrix.pivot.exists_is_two_block_diagonal_list_transvec_mul_mul_list_transvec Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
+-/
 
+#print Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction /-
 /-- Inductive step for the reduction: if one knows that any size `r` matrix can be reduced to
 diagonal form by elementary operations, then one deduces it for matrices over `fin r ⊕ unit`. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
@@ -661,9 +876,16 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
   rw [this]
   simp [h₀]
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
+-/
 
 variable {n p} [Fintype n] [Fintype p]
 
+/- warning: matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal -> Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {p : Type.{u2}} {𝕜 : Type.{u3}} [_inst_1 : Field.{u3} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u2} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u2} p] (M : Matrix.{u2, u2, u3} p p 𝕜) (e : Equiv.{succ u2, succ u1} p n), (Exists.{succ (max u1 u3)} (List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L : List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{succ (max u1 u3)} (List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u3} (Matrix.TransvectionStruct.{u3, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u3)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u3)} (Matrix.{u1, u1, u3} n n 𝕜) (Matrix.mul.{u3, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))))) (Matrix.mul.{u3, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u3} 𝕜 (Ring.toDistrib.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (DivisionRing.toRing.{u3} 𝕜 (Field.toDivisionRing.{u3} 𝕜 _inst_1)))))) (List.prod.{max u1 u3} 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(Field.toDivisionRing.{u3} 𝕜 _inst_1))))))) D)))))
+but is expected to have type
+  forall {n : Type.{u1}} {p : Type.{u3}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : DecidableEq.{succ u3} p] [_inst_5 : Fintype.{u1} n] [_inst_6 : Fintype.{u3} p] (M : Matrix.{u3, u3, u2} p p 𝕜) (e : Equiv.{succ u3, succ u1} p n), (Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜)) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), max (succ u3) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) 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(CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Matrix.{u3, u3, u2} p p 𝕜) (fun (_x : Matrix.{u3, u3, u2} p p 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u3, u3, u2} p p 𝕜) => Matrix.{u1, u1, u2} n n 𝕜) _x) (SMulHomClass.toFunLike.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (SMulZeroClass.toSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toZero.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (AddMonoid.toAddZeroClass.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) 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(Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (SMulZeroClass.toSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toZero.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AddCommMonoid.toAddMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (MonoidWithZero.toMonoid.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)))) (Module.toDistribMulAction.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Semiring.toNonAssocSemiring.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b))))) (Algebra.toModule.{u2, max u3 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (Module.toDistribMulAction.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u2, max u1 u2} 𝕜 (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u2, max u1 u2, max (max u1 u3) u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (AlgEquivClass.toAlgHomClass.{max (max u1 u3) u2, u2, max u3 u2, max u1 u2} (AlgEquiv.{u2, max u2 u3, max u2 u1} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) 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_inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u2, max u1 u2} 𝕜 (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Matrix.semiring.{u2, u3} p 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_6 (fun (a : p) (b : p) => _inst_3 a b)) (Matrix.semiring.{u2, u1} n 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) _inst_5 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u2, u3, u2} p 𝕜 𝕜 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Matrix.instAlgebraMatrixSemiring.{u2, u1, u2} n 𝕜 𝕜 _inst_5 (fun (a : n) (b : n) => _inst_2 a b) (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Algebra.id.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))))))) (Matrix.reindexAlgEquiv.{u3, u1, u2} p n 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) _inst_5 _inst_6 (fun (a : p) (b : p) => _inst_3 a b) (fun (a : n) (b : n) => _inst_2 a b) e) M)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.instMulMatrix.{u2, u1} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D))))) -> (Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) (fun (L' : List.{max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜)) => Exists.{max (succ u3) (succ u2)} (p -> 𝕜) (fun (D : p -> 𝕜) => Eq.{max (succ u3) (succ u2)} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.mul.{u2, u3, u3, u3} p p p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u3 u2} (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.instMulMatrix.{u2, u3} p 𝕜 _inst_6 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.one.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))) (List.map.{max u3 u2, max u3 u2} (Matrix.TransvectionStruct.{u2, u3} p 𝕜) (Matrix.{u3, u3, u2} p p 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u3} p 𝕜 (fun (a : p) (b : p) => _inst_3 a b) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) D)))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Reduction to diagonal form by elementary operations is invariant under reindexing. -/
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)
     (e : p ≃ n)
@@ -685,6 +907,7 @@ theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matr
   simp only [Equiv.symm_symm, reindex_apply, submatrix_diagonal_equiv, reindex_alg_equiv_apply]
 #align matrix.pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal
 
+#print Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux /-
 /-- Any matrix can be reduced to diagonal form by elementary operations. Formulated here on `Type 0`
 because we will make an induction using `fin r`.
 See `exists_list_transvec_mul_mul_list_transvec_eq_diagonal` for the general version (which follows
@@ -710,7 +933,14 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
       exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction fun N =>
         IH (Fin r) N (by simp)
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
+-/
 
+/- warning: matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal -> Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (M : Matrix.{u1, u1, u2} n n 𝕜), Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) M) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D))))
+but is expected to have type
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n 𝕜), Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L' : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) M) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonalₓ'. -/
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
@@ -721,6 +951,12 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
   apply exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal
 
+/- warning: matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec -> Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (M : Matrix.{u1, u1, u2} n n 𝕜), Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{succ (max u1 u2)} (List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) (fun (L' : List.{max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)))) => Exists.{max (succ u1) (succ u2)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n n 𝕜) M (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L)) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D)) (List.prod.{max u1 u2} (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.hasMul.{u2, u1} n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (Matrix.hasOne.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) (AddMonoidWithOne.toOne.{u2} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u2} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u2} 𝕜 (Ring.toAddCommGroupWithOne.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1))))))) (List.map.{max u1 u2, max u1 u2} (Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) (Matrix.{u1, u1, u2} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))) L'))))))
+but is expected to have type
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n 𝕜), Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) (fun (L' : List.{max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜)) => Exists.{max (succ u2) (succ u1)} (n -> 𝕜) (fun (D : n -> 𝕜) => Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n n 𝕜) M (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L)) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D)) (List.prod.{max u2 u1} (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.instMulMatrix.{u1, u2} n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))))) (Matrix.one.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (List.map.{max u2 u1, max u2 u1} (Matrix.TransvectionStruct.{u1, u2} n 𝕜) (Matrix.{u2, u2, u1} n n 𝕜) (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))) L'))))))
+Case conversion may be inaccurate. Consider using '#align matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvecₓ'. -/
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
 transvections.-/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
@@ -743,6 +979,12 @@ open Pivot TransvectionStruct
 
 variable {n} [Fintype n]
 
+/- warning: matrix.diagonal_transvection_induction -> Matrix.diagonal_transvection_induction is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (P : (Matrix.{u1, u1, u2} n n 𝕜) -> Prop) (M : Matrix.{u1, u1, u2} n n 𝕜), (forall (D : n -> 𝕜), (Eq.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) M)) -> (P (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D))) -> (forall (t : Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))), P (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) t)) -> (forall (A : Matrix.{u1, u1, u2} n n 𝕜) (B : Matrix.{u1, u1, u2} n n 𝕜), (P A) -> (P B) -> (P (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) A B))) -> (P M)
+but is expected to have type
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (P : (Matrix.{u2, u2, u1} n n 𝕜) -> Prop) (M : Matrix.{u2, u2, u1} n n 𝕜), (forall (D : n -> 𝕜), (Eq.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) M)) -> (P (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D))) -> (forall (t : Matrix.TransvectionStruct.{u1, u2} n 𝕜), P (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) t)) -> (forall (A : Matrix.{u2, u2, u1} n n 𝕜) (B : Matrix.{u2, u2, u1} n n 𝕜), (P A) -> (P B) -> (P (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) A B))) -> (P M)
+Case conversion may be inaccurate. Consider using '#align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_inductionₓ'. -/
 /-- Induction principle for matrices based on transvections: if a property is true for all diagonal
 matrices, all transvections, and is stable under product, then it is true for all matrices. This is
 the useful way to say that matrices are generated by diagonal matrices and transvections.
@@ -775,6 +1017,12 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
     exact hmul _ _ (htransvec _) IH
 #align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_induction
 
+/- warning: matrix.diagonal_transvection_induction_of_det_ne_zero -> Matrix.diagonal_transvection_induction_of_det_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {n : Type.{u1}} {𝕜 : Type.{u2}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : DecidableEq.{succ u1} n] [_inst_5 : Fintype.{u1} n] (P : (Matrix.{u1, u1, u2} n n 𝕜) -> Prop) (M : Matrix.{u1, u1, u2} n n 𝕜), (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) 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_1))))))))))) -> (forall (D : n -> 𝕜), (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D)) (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_1))))))))))) -> (P (Matrix.diagonal.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (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_1))))))) D))) -> (forall (t : Matrix.TransvectionStruct.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))), P (Matrix.TransvectionStruct.toMatrix.{u2, u1} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) t)) -> (forall (A : Matrix.{u1, u1, u2} n n 𝕜) (B : Matrix.{u1, u1, u2} n n 𝕜), (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) A) (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_1))))))))))) -> (Ne.{succ u2} 𝕜 (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) B) (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_1))))))))))) -> (P A) -> (P B) -> (P (Matrix.mul.{u2, u1, u1, u1} n n n 𝕜 _inst_5 (Distrib.toHasMul.{u2} 𝕜 (Ring.toDistrib.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (DivisionRing.toRing.{u2} 𝕜 (Field.toDivisionRing.{u2} 𝕜 _inst_1)))))) A B))) -> (P M)
+but is expected to have type
+  forall {n : Type.{u2}} {𝕜 : Type.{u1}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : DecidableEq.{succ u2} n] [_inst_5 : Fintype.{u2} n] (P : (Matrix.{u2, u2, u1} n n 𝕜) -> Prop) (M : Matrix.{u2, u2, u1} n n 𝕜), (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) M) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (forall (D : n -> 𝕜), (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (P (Matrix.diagonal.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) D))) -> (forall (t : Matrix.TransvectionStruct.{u1, u2} n 𝕜), P (Matrix.TransvectionStruct.toMatrix.{u1, u2} n 𝕜 (fun (a : n) (b : n) => _inst_2 a b) (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) t)) -> (forall (A : Matrix.{u2, u2, u1} n n 𝕜) (B : Matrix.{u2, u2, u1} n n 𝕜), (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) A) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (Ne.{succ u1} 𝕜 (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_2 a b) _inst_5 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) B) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) -> (P A) -> (P B) -> (P (Matrix.mul.{u1, u2, u2, u2} n n n 𝕜 _inst_5 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))) A B))) -> (P M)
+Case conversion may be inaccurate. Consider using '#align matrix.diagonal_transvection_induction_of_det_ne_zero Matrix.diagonal_transvection_induction_of_det_ne_zeroₓ'. -/
 /-- Induction principle for invertible matrices based on transvections: if a property is true for
 all invertible diagonal matrices, all transvections, and is stable under product of invertible
 matrices, then it is true for all invertible matrices. This is the useful way to say that

mathlib commit https://github.com/leanprover-community/mathlib/commit/0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.transvection
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -104,16 +104,16 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
   ext (a b)
   by_cases ha : i = a; by_cases hb : j = b
   ·
-    simp only [update_row, transvection, ha, hb, Function.update_same, std_basis_matrix.apply_same,
-      Pi.add_apply, one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul]
+    simp only [update_row_self, transvection, ha, hb, Pi.add_apply, std_basis_matrix.apply_same,
+      one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul]
   ·
-    simp only [update_row, transvection, ha, hb, std_basis_matrix.apply_of_ne, Function.update_same,
-      Pi.add_apply, Ne.def, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne,
-      Algebra.id.smul_eq_mul, MulZeroClass.mul_zero]
+    simp only [update_row_self, transvection, ha, hb, std_basis_matrix.apply_of_ne, Pi.add_apply,
+      Ne.def, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne, Algebra.id.smul_eq_mul,
+      MulZeroClass.mul_zero]
   ·
-    simp only [update_row, transvection, ha, Ne.symm ha, std_basis_matrix.apply_of_ne, add_zero,
-      Algebra.id.smul_eq_mul, Function.update_noteq, Ne.def, not_false_iff, DMatrix.add_apply,
-      Pi.smul_apply, MulZeroClass.mul_zero, false_and_iff]
+    simp only [update_row_ne, transvection, ha, Ne.symm ha, std_basis_matrix.apply_of_ne, add_zero,
+      Algebra.id.smul_eq_mul, Ne.def, not_false_iff, DMatrix.add_apply, Pi.smul_apply,
+      MulZeroClass.mul_zero, false_and_iff]
 #align matrix.update_row_eq_transvection Matrix.updateRow_eq_transvection
 
 variable [Fintype n]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -703,7 +703,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
       by
       refine' Fintype.equivOfCardEq _
       rw [hn]
-      convert (@Fintype.card_sum (Fin r) Unit _ _).symm
+      convert(@Fintype.card_sum (Fin r) Unit _ _).symm
       simp
     apply reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal M e
     apply

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

@@ -109,11 +109,11 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
   ·
     simp only [update_row, transvection, ha, hb, std_basis_matrix.apply_of_ne, Function.update_same,
       Pi.add_apply, Ne.def, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne,
-      Algebra.id.smul_eq_mul, mul_zero]
+      Algebra.id.smul_eq_mul, MulZeroClass.mul_zero]
   ·
     simp only [update_row, transvection, ha, Ne.symm ha, std_basis_matrix.apply_of_ne, add_zero,
       Algebra.id.smul_eq_mul, Function.update_noteq, Ne.def, not_false_iff, DMatrix.add_apply,
-      Pi.smul_apply, mul_zero, false_and_iff]
+      Pi.smul_apply, MulZeroClass.mul_zero, false_and_iff]
 #align matrix.update_row_eq_transvection Matrix.updateRow_eq_transvection
 
 variable [Fintype n]

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -96,12 +96,13 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
       transvection i j c := by
   cases nonempty_fintype n
   ext a b
-  by_cases ha : i = a; by_cases hb : j = b
-  · simp only [updateRow_self, transvection, ha, hb, Pi.add_apply, StdBasisMatrix.apply_same,
-      one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul, add_apply]
-  · simp only [updateRow_self, transvection, ha, hb, StdBasisMatrix.apply_of_ne, Pi.add_apply,
-      Ne, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne, Algebra.id.smul_eq_mul,
-      mul_zero, add_apply]
+  by_cases ha : i = a
+  · by_cases hb : j = b
+    · simp only [updateRow_self, transvection, ha, hb, Pi.add_apply, StdBasisMatrix.apply_same,
+        one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul, add_apply]
+    · simp only [updateRow_self, transvection, ha, hb, StdBasisMatrix.apply_of_ne, Pi.add_apply,
+        Ne, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne, Algebra.id.smul_eq_mul,
+        mul_zero, add_apply]
   · simp only [updateRow_ne, transvection, ha, Ne.symm ha, StdBasisMatrix.apply_of_ne, add_zero,
       Algebra.id.smul_eq_mul, Ne, not_false_iff, DMatrix.add_apply, Pi.smul_apply,
       mul_zero, false_and_iff, add_apply]

@@ -373,8 +373,7 @@ theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk :
   refine' Nat.decreasingInduction' _ hk _
   · intro n hn _ IH
     have hn' : n < (listTransvecCol M).length := by simpa [listTransvecCol] using hn
-    -- Porting note: after changing from `nthLe` to `get`, we need to provide all arguments
-    rw [← @List.cons_get_drop_succ _ _ ⟨n, hn'⟩]
+    rw [List.drop_eq_get_cons hn']
     simpa [listTransvecCol, Matrix.mul_assoc]
   · simp only [listTransvecCol, List.length_ofFn, le_refl, List.drop_eq_nil_of_le, List.prod_nil,
       Matrix.one_mul]
@@ -402,8 +401,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
   · intro n hn hk IH
     have hn' : n < (listTransvecCol M).length := by simpa [listTransvecCol] using hn
     let n' : Fin r := ⟨n, hn⟩
-    -- Porting note: after changing from `nthLe` to `get`, we need to provide all arguments
-    rw [← @List.cons_get_drop_succ _ _ ⟨n, hn'⟩]
+    rw [List.drop_eq_get_cons hn']
     have A :
       (listTransvecCol M).get ⟨n, hn'⟩ =
         transvection (inl n') (inr unit) (-M (inl n') (inr unit) / M (inr unit) (inr unit)) :=

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

@@ -148,7 +148,7 @@ variable (R n)
 /-- A structure containing all the information from which one can build a nontrivial transvection.
 This structure is easier to manipulate than transvections as one has a direct access to all the
 relevant fields. -/
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 structure TransvectionStruct where
   (i j : n)
   hij : i ≠ j

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -234,7 +234,7 @@ theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
     simp_rw [IH, Matrix.mul_one, t.mul_inv]
 #align matrix.transvection_struct.prod_mul_reverse_inv_prod Matrix.TransvectionStruct.prod_mul_reverse_inv_prod
 
-/-- `M` is a scalar matrix if it commutes with every nontrivial transvection (elementary matrix).-/
+/-- `M` is a scalar matrix if it commutes with every nontrivial transvection (elementary matrix). -/
 theorem _root_.Matrix.mem_range_scalar_of_commute_transvectionStruct {M : Matrix n n R}
     (hM : ∀ t : TransvectionStruct n R, Commute t.toMatrix M) :
     M ∈ Set.range (Matrix.scalar n) := by
@@ -690,7 +690,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
 #align matrix.pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal
 
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
-transvections.-/
+transvections. -/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       M = (L.map toMatrix).prod * diagonal D * (L'.map toMatrix).prod := by

@@ -100,10 +100,10 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
   · simp only [updateRow_self, transvection, ha, hb, Pi.add_apply, StdBasisMatrix.apply_same,
       one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul, add_apply]
   · simp only [updateRow_self, transvection, ha, hb, StdBasisMatrix.apply_of_ne, Pi.add_apply,
-      Ne.def, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne, Algebra.id.smul_eq_mul,
+      Ne, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne, Algebra.id.smul_eq_mul,
       mul_zero, add_apply]
   · simp only [updateRow_ne, transvection, ha, Ne.symm ha, StdBasisMatrix.apply_of_ne, add_zero,
-      Algebra.id.smul_eq_mul, Ne.def, not_false_iff, DMatrix.add_apply, Pi.smul_apply,
+      Algebra.id.smul_eq_mul, Ne, not_false_iff, DMatrix.add_apply, Pi.smul_apply,
       mul_zero, false_and_iff, add_apply]
 #align matrix.update_row_eq_transvection Matrix.updateRow_eq_transvection
 
@@ -449,7 +449,7 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
     simp only [List.take_succ, ← Matrix.mul_assoc, this, List.prod_append, Matrix.mul_one,
       List.prod_cons, List.prod_nil, Option.toList_some]
     rw [mul_transvection_apply_of_ne, IH hkr.le]
-    simp only [Ne.def, not_false_iff]
+    simp only [Ne, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
 
 /-- Multiplying by all the matrices in `listTransvecRow M` does not change the last column. -/
@@ -498,7 +498,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         rintro rfl
         cases i
         tauto
-      simp only [IH hnr.le, Ne.def, mul_transvection_apply_of_ne, Ne.symm h, inl.injEq,
+      simp only [IH hnr.le, Ne, mul_transvection_apply_of_ne, Ne.symm h, inl.injEq,
         not_false_eq_true]
       rcases le_or_lt (n + 1) i with (hi | hi)
       · simp [hi, n.le_succ.trans hi, if_true]

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -68,9 +68,7 @@ namespace Matrix
 open Matrix
 
 variable (n p : Type*) (R : Type u₂) {𝕜 : Type*} [Field 𝕜]
-
 variable [DecidableEq n] [DecidableEq p]
-
 variable [CommRing R]
 
 section Transvection

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -449,7 +449,7 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
             (-M (inr Unit.unit) (inl k') / M (inr Unit.unit) (inr Unit.unit))) := by
       simp only [listTransvecRow, List.ofFnNthVal, hkr, dif_pos, List.get?_ofFn]
     simp only [List.take_succ, ← Matrix.mul_assoc, this, List.prod_append, Matrix.mul_one,
-      List.prod_cons, List.prod_nil, Option.to_list_some]
+      List.prod_cons, List.prod_nil, Option.toList_some]
     rw [mul_transvection_apply_of_ne, IH hkr.le]
     simp only [Ne.def, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
@@ -486,7 +486,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         (-M (inr unit) (inl n') / M (inr unit) (inr unit))) := by
       simp only [listTransvecRow, List.ofFnNthVal, hnr, dif_pos, List.get?_ofFn]
     simp only [List.take_succ, A, ← Matrix.mul_assoc, List.prod_append, Matrix.mul_one,
-      List.prod_cons, List.prod_nil, Option.to_list_some]
+      List.prod_cons, List.prod_nil, Option.toList_some]
     by_cases h : n' = i
     · have hni : n = i := by
         cases i

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -371,11 +371,11 @@ def listTransvecRow : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
 /-- Multiplying by some of the matrices in `listTransvecCol M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
     (((listTransvecCol M).drop k).prod * M) (inr unit) i = M (inr unit) i := by
-  -- porting note: `apply` didn't work anymore, because of the implicit arguments
+  -- Porting note: `apply` didn't work anymore, because of the implicit arguments
   refine' Nat.decreasingInduction' _ hk _
   · intro n hn _ IH
     have hn' : n < (listTransvecCol M).length := by simpa [listTransvecCol] using hn
-    -- porting note: after changing from `nthLe` to `get`, we need to provide all arguments
+    -- Porting note: after changing from `nthLe` to `get`, we need to provide all arguments
     rw [← @List.cons_get_drop_succ _ _ ⟨n, hn'⟩]
     simpa [listTransvecCol, Matrix.mul_assoc]
   · simp only [listTransvecCol, List.length_ofFn, le_refl, List.drop_eq_nil_of_le, List.prod_nil,
@@ -399,12 +399,12 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
           if k ≤ i then 0 else M (inl i) (inr unit) by
     simpa only [List.drop, _root_.zero_le, ite_true] using H 0 (zero_le _)
   intro k hk
-  -- porting note: `apply` didn't work anymore, because of the implicit arguments
+  -- Porting note: `apply` didn't work anymore, because of the implicit arguments
   refine' Nat.decreasingInduction' _ hk _
   · intro n hn hk IH
     have hn' : n < (listTransvecCol M).length := by simpa [listTransvecCol] using hn
     let n' : Fin r := ⟨n, hn⟩
-    -- porting note: after changing from `nthLe` to `get`, we need to provide all arguments
+    -- Porting note: after changing from `nthLe` to `get`, we need to provide all arguments
     rw [← @List.cons_get_drop_succ _ _ ⟨n, hn'⟩]
     have A :
       (listTransvecCol M).get ⟨n, hn'⟩ =
@@ -629,7 +629,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
       diagonal (Sum.elim D₀ fun _ => c) by
     simpa [M', c, Matrix.mul_assoc]
   have : M' = fromBlocks M'' 0 0 (diagonal fun _ => c) := by
-    -- porting note: simplified proof, because `congr` didn't work anymore
+    -- Porting note: simplified proof, because `congr` didn't work anymore
     rw [← fromBlocks_toBlocks M', hM.1, hM.2]
     rfl
   rw [this]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -414,7 +414,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
     by_cases h : n' = i
     · have hni : n = i := by
         cases i
-        simp only [Fin.mk_eq_mk] at h
+        simp only [n', Fin.mk_eq_mk] at h
         simp [h]
       simp only [h, transvection_mul_apply_same, IH, ← hni, add_le_iff_nonpos_right,
           listTransvecCol_mul_last_row_drop _ _ hn]
@@ -490,7 +490,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
     by_cases h : n' = i
     · have hni : n = i := by
         cases i
-        simp only [Fin.mk_eq_mk] at h
+        simp only [n', Fin.mk_eq_mk] at h
         simp only [h]
       have : ¬n.succ ≤ i := by simp only [← hni, n.lt_succ_self, not_le]
       simp only [h, mul_transvection_apply_same, List.take, if_false,
@@ -559,8 +559,8 @@ theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0
     List.ofFn fun i : Fin r =>
       ⟨inr unit, inl i, by simp, -M (inr unit) (inl i) / M (inr unit) (inr unit)⟩
   refine' ⟨L, L', _⟩
-  have A : L.map toMatrix = listTransvecCol M := by simp [listTransvecCol, (· ∘ ·)]
-  have B : L'.map toMatrix = listTransvecRow M := by simp [listTransvecRow, (· ∘ ·)]
+  have A : L.map toMatrix = listTransvecCol M := by simp [L, listTransvecCol, (· ∘ ·)]
+  have B : L'.map toMatrix = listTransvecRow M := by simp [L', listTransvecRow, (· ∘ ·)]
   rw [A, B]
   exact isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow M hM
 #align matrix.pivot.exists_is_two_block_diagonal_of_ne_zero Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero
@@ -591,7 +591,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
       exact (H j).2
   rcases this with ⟨i, h | h⟩
   · let M' := transvection (inr Unit.unit) (inl i) 1 * M
-    have hM' : M' (inr unit) (inr unit) ≠ 0 := by simpa [hM]
+    have hM' : M' (inr unit) (inr unit) ≠ 0 := by simpa [M', hM]
     rcases exists_isTwoBlockDiagonal_of_ne_zero M' hM' with ⟨L, L', hLL'⟩
     rw [Matrix.mul_assoc] at hLL'
     refine' ⟨L ++ [⟨inr unit, inl i, by simp, 1⟩], L', _⟩
@@ -599,7 +599,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
       List.prod_nil, List.map, Matrix.mul_assoc (L.map toMatrix).prod]
     exact hLL'
   · let M' := M * transvection (inl i) (inr unit) 1
-    have hM' : M' (inr unit) (inr unit) ≠ 0 := by simpa [hM]
+    have hM' : M' (inr unit) (inr unit) ≠ 0 := by simpa [M', hM]
     rcases exists_isTwoBlockDiagonal_of_ne_zero M' hM' with ⟨L, L', hLL'⟩
     refine' ⟨L, ⟨inl i, inr unit, by simp, 1⟩::L', _⟩
     simp only [← Matrix.mul_assoc, toMatrix_mk, List.prod_cons, List.map]
@@ -627,7 +627,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
       Sum.elim D₀ fun _ => M' (inr unit) (inr unit), _⟩
   suffices (L₀.map (toMatrix ∘ sumInl Unit)).prod * M' * (L₀'.map (toMatrix ∘ sumInl Unit)).prod =
       diagonal (Sum.elim D₀ fun _ => c) by
-    simpa [Matrix.mul_assoc]
+    simpa [M', c, Matrix.mul_assoc]
   have : M' = fromBlocks M'' 0 0 (diagonal fun _ => c) := by
     -- porting note: simplified proof, because `congr` didn't work anymore
     rw [← fromBlocks_toBlocks M', hM.1, hM.2]

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

@@ -150,7 +150,7 @@ variable (R n)
 /-- A structure containing all the information from which one can build a nontrivial transvection.
 This structure is easier to manipulate than transvections as one has a direct access to all the
 relevant fields. -/
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 structure TransvectionStruct where
   (i j : n)
   hij : i ≠ j

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -396,8 +396,8 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
     ∀ k : ℕ,
       k ≤ r →
         (((listTransvecCol M).drop k).prod * M) (inl i) (inr unit) =
-          if k ≤ i then 0 else M (inl i) (inr unit)
-  · simpa only [List.drop, _root_.zero_le, ite_true] using H 0 (zero_le _)
+          if k ≤ i then 0 else M (inl i) (inr unit) by
+    simpa only [List.drop, _root_.zero_le, ite_true] using H 0 (zero_le _)
   intro k hk
   -- porting note: `apply` didn't work anymore, because of the implicit arguments
   refine' Nat.decreasingInduction' _ hk _
@@ -470,8 +470,8 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
     ∀ k : ℕ,
       k ≤ r →
         (M * ((listTransvecRow M).take k).prod) (inr unit) (inl i) =
-          if k ≤ i then M (inr unit) (inl i) else 0
-  · have A : (listTransvecRow M).length = r := by simp [listTransvecRow]
+          if k ≤ i then M (inr unit) (inl i) else 0 by
+    have A : (listTransvecRow M).length = r := by simp [listTransvecRow]
     rw [← List.take_length (listTransvecRow M), A]
     have : ¬r ≤ i := by simp
     simpa only [this, ite_eq_right_iff] using H r le_rfl
@@ -727,8 +727,8 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
   have PD : P (diagonal D) := hdiag D (by simp [h])
   suffices H :
     ∀ (L₁ L₂ : List (TransvectionStruct n 𝕜)) (E : Matrix n n 𝕜),
-      P E → P ((L₁.map toMatrix).prod * E * (L₂.map toMatrix).prod)
-  · rw [h]
+      P E → P ((L₁.map toMatrix).prod * E * (L₂.map toMatrix).prod) by
+    rw [h]
     apply H L L'
     exact PD
   intro L₁ L₂ E PE

M is a scalar matrix if it commutes with every nontrivial transvection (elementary matrix).

Also adds iff versions and corrects the names of the lemmas in #7810

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

Co-authored-by: Wen Yang <yang-wen@139.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -236,6 +236,22 @@ theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
     simp_rw [IH, Matrix.mul_one, t.mul_inv]
 #align matrix.transvection_struct.prod_mul_reverse_inv_prod Matrix.TransvectionStruct.prod_mul_reverse_inv_prod
 
+/-- `M` is a scalar matrix if it commutes with every nontrivial transvection (elementary matrix).-/
+theorem _root_.Matrix.mem_range_scalar_of_commute_transvectionStruct {M : Matrix n n R}
+    (hM : ∀ t : TransvectionStruct n R, Commute t.toMatrix M) :
+    M ∈ Set.range (Matrix.scalar n) := by
+  refine mem_range_scalar_of_commute_stdBasisMatrix ?_
+  intro i j hij
+  simpa [transvection, mul_add, add_mul] using (hM ⟨i, j, hij, 1⟩).eq
+
+theorem _root_.Matrix.mem_range_scalar_iff_commute_transvectionStruct {M : Matrix n n R} :
+    M ∈ Set.range (Matrix.scalar n) ↔ ∀ t : TransvectionStruct n R, Commute t.toMatrix M := by
+  refine ⟨fun h t => ?_, mem_range_scalar_of_commute_transvectionStruct⟩
+  rw [mem_range_scalar_iff_commute_stdBasisMatrix] at h
+  refine (Commute.one_left M).add_left ?_
+  convert (h _ _ t.hij).smul_left t.c using 1
+  rw [smul_stdBasisMatrix, smul_eq_mul, mul_one]
+
 end
 
 open Sum

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -484,7 +484,8 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         rintro rfl
         cases i
         tauto
-      simp only [IH hnr.le, Ne.def, mul_transvection_apply_of_ne, Ne.symm h, inl.injEq]
+      simp only [IH hnr.le, Ne.def, mul_transvection_apply_of_ne, Ne.symm h, inl.injEq,
+        not_false_eq_true]
       rcases le_or_lt (n + 1) i with (hi | hi)
       · simp [hi, n.le_succ.trans hi, if_true]
       · rw [if_neg, if_neg]

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

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

@@ -103,10 +103,10 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
       one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul, add_apply]
   · simp only [updateRow_self, transvection, ha, hb, StdBasisMatrix.apply_of_ne, Pi.add_apply,
       Ne.def, not_false_iff, Pi.smul_apply, and_false_iff, one_apply_ne, Algebra.id.smul_eq_mul,
-      MulZeroClass.mul_zero, add_apply]
+      mul_zero, add_apply]
   · simp only [updateRow_ne, transvection, ha, Ne.symm ha, StdBasisMatrix.apply_of_ne, add_zero,
       Algebra.id.smul_eq_mul, Ne.def, not_false_iff, DMatrix.add_apply, Pi.smul_apply,
-      MulZeroClass.mul_zero, false_and_iff, add_apply]
+      mul_zero, false_and_iff, add_apply]
 #align matrix.update_row_eq_transvection Matrix.updateRow_eq_transvection
 
 variable [Fintype n]

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).

@@ -23,7 +23,7 @@ algorithms operating on rows and columns.
 Transvections are a special case of *elementary matrices* (according to most references, these also
 contain the matrices exchanging rows, and the matrices multiplying a row by a constant).
 
-We show that, over a field, any matrix can be written as `L ⬝ D ⬝ L'`, where `L` and `L'` are
+We show that, over a field, any matrix can be written as `L * D * L'`, where `L` and `L'` are
 products of transvections and `D` is diagonal. In other words, one can reduce a matrix to diagonal
 form by operations on its rows and columns, a variant of Gauss' pivot algorithm.
 
@@ -35,7 +35,7 @@ form by operations on its rows and columns, a variant of Gauss' pivot algorithm.
   arguments.
 
 * `exists_list_transvec_mul_diagonal_mul_list_transvec` states that any matrix `M` over a field can
-  be written in the form `t_1 ⬝ ... ⬝ t_k ⬝ D ⬝ t'_1 ⬝ ... ⬝ t'_l`, where `D` is diagonal and
+  be written in the form `t_1 * ... * t_k * D * t'_1 * ... * t'_l`, where `D` is diagonal and
   the `t_i`, `t'_j` are transvections.
 
 * `diagonal_transvection_induction` shows that a property which is true for diagonal matrices and
@@ -78,7 +78,7 @@ section Transvection
 variable {R n} (i j : n)
 
 /-- The transvection matrix `Transvection i j c` is equal to the identity plus `c` at position
-`(i, j)`. Multiplying by it on the left (as in `Transvection i j c ⬝ M`) corresponds to adding
+`(i, j)`. Multiplying by it on the left (as in `Transvection i j c * M`) corresponds to adding
 `c` times the `j`-th line of `M` to its `i`-th line. Multiplying by it on the right corresponds
 to adding `c` times the `i`-th column to the `j`-th column. -/
 def transvection (c : R) : Matrix n n R :=
@@ -112,30 +112,30 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
 variable [Fintype n]
 
 theorem transvection_mul_transvection_same (h : i ≠ j) (c d : R) :
-    transvection i j c ⬝ transvection i j d = transvection i j (c + d) := by
+    transvection i j c * transvection i j d = transvection i j (c + d) := by
   simp [transvection, Matrix.add_mul, Matrix.mul_add, h, h.symm, add_smul, add_assoc,
     stdBasisMatrix_add]
 #align matrix.transvection_mul_transvection_same Matrix.transvection_mul_transvection_same
 
 @[simp]
 theorem transvection_mul_apply_same (b : n) (c : R) (M : Matrix n n R) :
-    (transvection i j c ⬝ M) i b = M i b + c * M j b := by simp [transvection, Matrix.add_mul]
+    (transvection i j c * M) i b = M i b + c * M j b := by simp [transvection, Matrix.add_mul]
 #align matrix.transvection_mul_apply_same Matrix.transvection_mul_apply_same
 
 @[simp]
 theorem mul_transvection_apply_same (a : n) (c : R) (M : Matrix n n R) :
-    (M ⬝ transvection i j c) a j = M a j + c * M a i := by
+    (M * transvection i j c) a j = M a j + c * M a i := by
   simp [transvection, Matrix.mul_add, mul_comm]
 #align matrix.mul_transvection_apply_same Matrix.mul_transvection_apply_same
 
 @[simp]
 theorem transvection_mul_apply_of_ne (a b : n) (ha : a ≠ i) (c : R) (M : Matrix n n R) :
-    (transvection i j c ⬝ M) a b = M a b := by simp [transvection, Matrix.add_mul, ha]
+    (transvection i j c * M) a b = M a b := by simp [transvection, Matrix.add_mul, ha]
 #align matrix.transvection_mul_apply_of_ne Matrix.transvection_mul_apply_of_ne
 
 @[simp]
 theorem mul_transvection_apply_of_ne (a b : n) (hb : b ≠ j) (c : R) (M : Matrix n n R) :
-    (M ⬝ transvection i j c) a b = M a b := by simp [transvection, Matrix.mul_add, hb]
+    (M * transvection i j c) a b = M a b := by simp [transvection, Matrix.mul_add, hb]
 #align matrix.mul_transvection_apply_of_ne Matrix.mul_transvection_apply_of_ne
 
 @[simp]
@@ -203,34 +203,34 @@ section
 
 variable [Fintype n]
 
-theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix ⬝ t.toMatrix = 1 := by
+theorem inv_mul (t : TransvectionStruct n R) : t.inv.toMatrix * t.toMatrix = 1 := by
   rcases t with ⟨_, _, t_hij⟩
   simp [toMatrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.inv_mul Matrix.TransvectionStruct.inv_mul
 
-theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix ⬝ t.inv.toMatrix = 1 := by
+theorem mul_inv (t : TransvectionStruct n R) : t.toMatrix * t.inv.toMatrix = 1 := by
   rcases t with ⟨_, _, t_hij⟩
   simp [toMatrix, transvection_mul_transvection_same, t_hij]
 #align matrix.transvection_struct.mul_inv Matrix.TransvectionStruct.mul_inv
 
 theorem reverse_inv_prod_mul_prod (L : List (TransvectionStruct n R)) :
-    (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod ⬝ (L.map toMatrix).prod = 1 := by
+    (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod * (L.map toMatrix).prod = 1 := by
   induction' L with t L IH
   · simp
   · suffices
-      (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod ⬝ (t.inv.toMatrix ⬝ t.toMatrix) ⬝
+      (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod * (t.inv.toMatrix * t.toMatrix) *
           (L.map toMatrix).prod = 1
       by simpa [Matrix.mul_assoc]
     simpa [inv_mul] using IH
 #align matrix.transvection_struct.reverse_inv_prod_mul_prod Matrix.TransvectionStruct.reverse_inv_prod_mul_prod
 
 theorem prod_mul_reverse_inv_prod (L : List (TransvectionStruct n R)) :
-    (L.map toMatrix).prod ⬝ (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod = 1 := by
+    (L.map toMatrix).prod * (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod = 1 := by
   induction' L with t L IH
   · simp
   · suffices
-      t.toMatrix ⬝
-            ((L.map toMatrix).prod ⬝ (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod) ⬝
+      t.toMatrix *
+            ((L.map toMatrix).prod * (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod) *
           t.inv.toMatrix = 1
       by simpa [Matrix.mul_assoc]
     simp_rw [IH, Matrix.mul_one, t.mul_inv]
@@ -263,8 +263,8 @@ theorem toMatrix_sumInl (t : TransvectionStruct n R) :
 @[simp]
 theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
-    (L.map (toMatrix ∘ sumInl p)).prod ⬝ fromBlocks M 0 0 N =
-      fromBlocks ((L.map toMatrix).prod ⬝ M) 0 0 N := by
+    (L.map (toMatrix ∘ sumInl p)).prod * fromBlocks M 0 0 N =
+      fromBlocks ((L.map toMatrix).prod * M) 0 0 N := by
   induction' L with t L IH
   · simp
   · simp [Matrix.mul_assoc, IH, toMatrix_sumInl, fromBlocks_multiply]
@@ -273,8 +273,8 @@ theorem sumInl_toMatrix_prod_mul [Fintype n] [Fintype p] (M : Matrix n n R)
 @[simp]
 theorem mul_sumInl_toMatrix_prod [Fintype n] [Fintype p] (M : Matrix n n R)
     (L : List (TransvectionStruct n R)) (N : Matrix p p R) :
-    fromBlocks M 0 0 N ⬝ (L.map (toMatrix ∘ sumInl p)).prod =
-      fromBlocks (M ⬝ (L.map toMatrix).prod) 0 0 N := by
+    fromBlocks M 0 0 N * (L.map (toMatrix ∘ sumInl p)).prod =
+      fromBlocks (M * (L.map toMatrix).prod) 0 0 N := by
   induction' L with t L IH generalizing M N
   · simp
   · simp [IH, toMatrix_sumInl, fromBlocks_multiply]
@@ -307,7 +307,7 @@ theorem toMatrix_reindexEquiv_prod (e : n ≃ p) (L : List (TransvectionStruct n
     (L.map (toMatrix ∘ reindexEquiv e)).prod = reindexAlgEquiv R e (L.map toMatrix).prod := by
   induction' L with t L IH
   · simp
-  · simp only [toMatrix_reindexEquiv, IH, Function.comp_apply, List.prod_cons, mul_eq_mul,
+  · simp only [toMatrix_reindexEquiv, IH, Function.comp_apply, List.prod_cons,
       reindexAlgEquiv_apply, List.map]
     exact (reindexAlgEquiv_mul _ _ _ _).symm
 #align matrix.transvection_struct.to_matrix_reindex_equiv_prod Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod
@@ -354,7 +354,7 @@ def listTransvecRow : List (Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
 
 /-- Multiplying by some of the matrices in `listTransvecCol M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
-    (((listTransvecCol M).drop k).prod ⬝ M) (inr unit) i = M (inr unit) i := by
+    (((listTransvecCol M).drop k).prod * M) (inr unit) i = M (inr unit) i := by
   -- porting note: `apply` didn't work anymore, because of the implicit arguments
   refine' Nat.decreasingInduction' _ hk _
   · intro n hn _ IH
@@ -368,18 +368,18 @@ theorem listTransvecCol_mul_last_row_drop (i : Sum (Fin r) Unit) {k : ℕ} (hk :
 
 /-- Multiplying by all the matrices in `listTransvecCol M` does not change the last row. -/
 theorem listTransvecCol_mul_last_row (i : Sum (Fin r) Unit) :
-    ((listTransvecCol M).prod ⬝ M) (inr unit) i = M (inr unit) i := by
+    ((listTransvecCol M).prod * M) (inr unit) i = M (inr unit) i := by
   simpa using listTransvecCol_mul_last_row_drop M i (zero_le _)
 #align matrix.pivot.list_transvec_col_mul_last_row Matrix.Pivot.listTransvecCol_mul_last_row
 
 /-- Multiplying by all the matrices in `listTransvecCol M` kills all the coefficients in the
 last column but the last one. -/
 theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
-    ((listTransvecCol M).prod ⬝ M) (inl i) (inr unit) = 0 := by
+    ((listTransvecCol M).prod * M) (inl i) (inr unit) = 0 := by
   suffices H :
     ∀ k : ℕ,
       k ≤ r →
-        (((listTransvecCol M).drop k).prod ⬝ M) (inl i) (inr unit) =
+        (((listTransvecCol M).drop k).prod * M) (inl i) (inr unit) =
           if k ≤ i then 0 else M (inl i) (inr unit)
   · simpa only [List.drop, _root_.zero_le, ite_true] using H 0 (zero_le _)
   intro k hk
@@ -394,7 +394,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
       (listTransvecCol M).get ⟨n, hn'⟩ =
         transvection (inl n') (inr unit) (-M (inl n') (inr unit) / M (inr unit) (inr unit)) :=
       by simp [listTransvecCol]
-    simp only [Matrix.mul_assoc, A, Matrix.mul_eq_mul, List.prod_cons]
+    simp only [Matrix.mul_assoc, A, List.prod_cons]
     by_cases h : n' = i
     · have hni : n = i := by
         cases i
@@ -422,7 +422,7 @@ theorem listTransvecCol_mul_last_col (hM : M (inr unit) (inr unit) ≠ 0) (i : F
 
 /-- Multiplying by some of the matrices in `listTransvecRow M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk : k ≤ r) :
-    (M ⬝ ((listTransvecRow M).take k).prod) i (inr unit) = M i (inr unit) := by
+    (M * ((listTransvecRow M).take k).prod) i (inr unit) = M i (inr unit) := by
   induction' k with k IH
   · simp only [Matrix.mul_one, List.take_zero, List.prod_nil, List.take, Matrix.mul_one]
   · have hkr : k < r := hk
@@ -433,14 +433,14 @@ theorem mul_listTransvecRow_last_col_take (i : Sum (Fin r) Unit) {k : ℕ} (hk :
             (-M (inr Unit.unit) (inl k') / M (inr Unit.unit) (inr Unit.unit))) := by
       simp only [listTransvecRow, List.ofFnNthVal, hkr, dif_pos, List.get?_ofFn]
     simp only [List.take_succ, ← Matrix.mul_assoc, this, List.prod_append, Matrix.mul_one,
-      Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
+      List.prod_cons, List.prod_nil, Option.to_list_some]
     rw [mul_transvection_apply_of_ne, IH hkr.le]
     simp only [Ne.def, not_false_iff]
 #align matrix.pivot.mul_list_transvec_row_last_col_take Matrix.Pivot.mul_listTransvecRow_last_col_take
 
 /-- Multiplying by all the matrices in `listTransvecRow M` does not change the last column. -/
 theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
-    (M ⬝ (listTransvecRow M).prod) i (inr unit) = M i (inr unit) := by
+    (M * (listTransvecRow M).prod) i (inr unit) = M i (inr unit) := by
   have A : (listTransvecRow M).length = r := by simp [listTransvecRow]
   rw [← List.take_length (listTransvecRow M), A]
   simpa using mul_listTransvecRow_last_col_take M i le_rfl
@@ -449,11 +449,11 @@ theorem mul_listTransvecRow_last_col (i : Sum (Fin r) Unit) :
 /-- Multiplying by all the matrices in `listTransvecRow M` kills all the coefficients in the
 last row but the last one. -/
 theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : Fin r) :
-    (M ⬝ (listTransvecRow M).prod) (inr unit) (inl i) = 0 := by
+    (M * (listTransvecRow M).prod) (inr unit) (inl i) = 0 := by
   suffices H :
     ∀ k : ℕ,
       k ≤ r →
-        (M ⬝ ((listTransvecRow M).take k).prod) (inr unit) (inl i) =
+        (M * ((listTransvecRow M).take k).prod) (inr unit) (inl i) =
           if k ≤ i then M (inr unit) (inl i) else 0
   · have A : (listTransvecRow M).length = r := by simp [listTransvecRow]
     rw [← List.take_length (listTransvecRow M), A]
@@ -470,7 +470,7 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
         (-M (inr unit) (inl n') / M (inr unit) (inr unit))) := by
       simp only [listTransvecRow, List.ofFnNthVal, hnr, dif_pos, List.get?_ofFn]
     simp only [List.take_succ, A, ← Matrix.mul_assoc, List.prod_append, Matrix.mul_one,
-      Matrix.mul_eq_mul, List.prod_cons, List.prod_nil, Option.to_list_some]
+      List.prod_cons, List.prod_nil, Option.to_list_some]
     by_cases h : n' = i
     · have hni : n = i := by
         cases i
@@ -496,8 +496,8 @@ theorem mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0) (i : F
 all the coefficients in the last row but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr unit) ≠ 0)
     (i : Fin r) :
-    ((listTransvecCol M).prod ⬝ M ⬝ (listTransvecRow M).prod) (inr unit) (inl i) = 0 := by
-  have : listTransvecRow M = listTransvecRow ((listTransvecCol M).prod ⬝ M) := by
+    ((listTransvecCol M).prod * M * (listTransvecRow M).prod) (inr unit) (inl i) = 0 := by
+  have : listTransvecRow M = listTransvecRow ((listTransvecCol M).prod * M) := by
     simp [listTransvecRow, listTransvecCol_mul_last_row]
   rw [this]
   apply mul_listTransvecRow_last_row
@@ -508,8 +508,8 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_col (hM : M (inr unit) (inr
 all the coefficients in the last column but the last one. -/
 theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr unit) ≠ 0)
     (i : Fin r) :
-    ((listTransvecCol M).prod ⬝ M ⬝ (listTransvecRow M).prod) (inl i) (inr unit) = 0 := by
-  have : listTransvecCol M = listTransvecCol (M ⬝ (listTransvecRow M).prod) := by
+    ((listTransvecCol M).prod * M * (listTransvecRow M).prod) (inl i) (inr unit) = 0 := by
+  have : listTransvecCol M = listTransvecCol (M * (listTransvecRow M).prod) := by
     simp [listTransvecCol, mul_listTransvecRow_last_col]
   rw [this, Matrix.mul_assoc]
   apply listTransvecCol_mul_last_col
@@ -520,7 +520,7 @@ theorem listTransvecCol_mul_mul_listTransvecRow_last_row (hM : M (inr unit) (inr
 the matrix in block-diagonal form. -/
 theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
     (hM : M (inr unit) (inr unit) ≠ 0) :
-    IsTwoBlockDiagonal ((listTransvecCol M).prod ⬝ M ⬝ (listTransvecRow M).prod) := by
+    IsTwoBlockDiagonal ((listTransvecCol M).prod * M * (listTransvecRow M).prod) := by
   constructor
   · ext i j
     have : j = unit := by simp only [eq_iff_true_of_subsingleton]
@@ -534,7 +534,7 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
 on the right makes a matrix block-diagonal, when the last coefficient is nonzero. -/
 theorem exists_isTwoBlockDiagonal_of_ne_zero (hM : M (inr unit) (inr unit) ≠ 0) :
     ∃ L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜),
-      IsTwoBlockDiagonal ((L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod) := by
+      IsTwoBlockDiagonal ((L.map toMatrix).prod * M * (L'.map toMatrix).prod) := by
   let L : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜) :=
     List.ofFn fun i : Fin r =>
       ⟨inl i, inr unit, by simp, -M (inl i) (inr unit) / M (inr unit) (inr unit)⟩
@@ -553,7 +553,7 @@ on the right makes a matrix block-diagonal. -/
 theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
     (M : Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
     ∃ L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜),
-      IsTwoBlockDiagonal ((L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod) := by
+      IsTwoBlockDiagonal ((L.map toMatrix).prod * M * (L'.map toMatrix).prod) := by
   by_cases H : IsTwoBlockDiagonal M
   · refine' ⟨List.nil, List.nil, by simpa using H⟩
   -- we have already proved this when the last coefficient is nonzero
@@ -573,19 +573,19 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
       rintro ⟨⟩ j
       exact (H j).2
   rcases this with ⟨i, h | h⟩
-  · let M' := transvection (inr Unit.unit) (inl i) 1 ⬝ M
+  · let M' := transvection (inr Unit.unit) (inl i) 1 * M
     have hM' : M' (inr unit) (inr unit) ≠ 0 := by simpa [hM]
     rcases exists_isTwoBlockDiagonal_of_ne_zero M' hM' with ⟨L, L', hLL'⟩
     rw [Matrix.mul_assoc] at hLL'
     refine' ⟨L ++ [⟨inr unit, inl i, by simp, 1⟩], L', _⟩
     simp only [List.map_append, List.prod_append, Matrix.mul_one, toMatrix_mk, List.prod_cons,
-      List.prod_nil, mul_eq_mul, List.map, Matrix.mul_assoc (L.map toMatrix).prod]
+      List.prod_nil, List.map, Matrix.mul_assoc (L.map toMatrix).prod]
     exact hLL'
-  · let M' := M ⬝ transvection (inl i) (inr unit) 1
+  · let M' := M * transvection (inl i) (inr unit) 1
     have hM' : M' (inr unit) (inr unit) ≠ 0 := by simpa [hM]
     rcases exists_isTwoBlockDiagonal_of_ne_zero M' hM' with ⟨L, L', hLL'⟩
     refine' ⟨L, ⟨inl i, inr unit, by simp, 1⟩::L', _⟩
-    simp only [← Matrix.mul_assoc, toMatrix_mk, List.prod_cons, mul_eq_mul, List.map]
+    simp only [← Matrix.mul_assoc, toMatrix_mk, List.prod_cons, List.map]
     rw [Matrix.mul_assoc (L.map toMatrix).prod]
     exact hLL'
 #align matrix.pivot.exists_is_two_block_diagonal_list_transvec_mul_mul_list_transvec Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
@@ -596,19 +596,19 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
     (IH :
       ∀ M : Matrix (Fin r) (Fin r) 𝕜,
         ∃ (L₀ L₀' : List (TransvectionStruct (Fin r) 𝕜)) (D₀ : Fin r → 𝕜),
-          (L₀.map toMatrix).prod ⬝ M ⬝ (L₀'.map toMatrix).prod = diagonal D₀)
+          (L₀.map toMatrix).prod * M * (L₀'.map toMatrix).prod = diagonal D₀)
     (M : Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
     ∃ (L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜)) (D : Sum (Fin r) Unit → 𝕜),
-      (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
+      (L.map toMatrix).prod * M * (L'.map toMatrix).prod = diagonal D := by
   rcases exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec M with ⟨L₁, L₁', hM⟩
-  let M' := (L₁.map toMatrix).prod ⬝ M ⬝ (L₁'.map toMatrix).prod
+  let M' := (L₁.map toMatrix).prod * M * (L₁'.map toMatrix).prod
   let M'' := toBlocks₁₁ M'
   rcases IH M'' with ⟨L₀, L₀', D₀, h₀⟩
   set c := M' (inr unit) (inr unit)
   refine'
     ⟨L₀.map (sumInl Unit) ++ L₁, L₁' ++ L₀'.map (sumInl Unit),
       Sum.elim D₀ fun _ => M' (inr unit) (inr unit), _⟩
-  suffices (L₀.map (toMatrix ∘ sumInl Unit)).prod ⬝ M' ⬝ (L₀'.map (toMatrix ∘ sumInl Unit)).prod =
+  suffices (L₀.map (toMatrix ∘ sumInl Unit)).prod * M' * (L₀'.map (toMatrix ∘ sumInl Unit)).prod =
       diagonal (Sum.elim D₀ fun _ => c) by
     simpa [Matrix.mul_assoc]
   have : M' = fromBlocks M'' 0 0 (diagonal fun _ => c) := by
@@ -626,10 +626,10 @@ theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matr
     (e : p ≃ n)
     (H :
       ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
-        (L.map toMatrix).prod ⬝ Matrix.reindexAlgEquiv 𝕜 e M ⬝ (L'.map toMatrix).prod =
+        (L.map toMatrix).prod * Matrix.reindexAlgEquiv 𝕜 e M * (L'.map toMatrix).prod =
           diagonal D) :
     ∃ (L L' : List (TransvectionStruct p 𝕜)) (D : p → 𝕜),
-      (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
+      (L.map toMatrix).prod * M * (L'.map toMatrix).prod = diagonal D := by
   rcases H with ⟨L₀, L₀', D₀, h₀⟩
   refine' ⟨L₀.map (reindexEquiv e.symm), L₀'.map (reindexEquiv e.symm), D₀ ∘ e, _⟩
   have : M = reindexAlgEquiv 𝕜 e.symm (reindexAlgEquiv 𝕜 e M) := by
@@ -648,7 +648,7 @@ from this one and reindexing). -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [Fintype n]
     [DecidableEq n] (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
-      (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
+      (L.map toMatrix).prod * M * (L'.map toMatrix).prod = diagonal D := by
   induction' hn : Fintype.card n with r IH generalizing n M
   · refine' ⟨List.nil, List.nil, fun _ => 1, _⟩
     ext i j
@@ -668,7 +668,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
-      (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
+      (L.map toMatrix).prod * M * (L'.map toMatrix).prod = diagonal D := by
   have e : n ≃ Fin (Fintype.card n) := Fintype.equivOfCardEq (by simp)
   apply reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal M e
   apply exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux
@@ -678,13 +678,13 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
 transvections.-/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
     ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
-      M = (L.map toMatrix).prod ⬝ diagonal D ⬝ (L'.map toMatrix).prod := by
+      M = (L.map toMatrix).prod * diagonal D * (L'.map toMatrix).prod := by
   rcases exists_list_transvec_mul_mul_list_transvec_eq_diagonal M with ⟨L, L', D, h⟩
   refine' ⟨L.reverse.map TransvectionStruct.inv, L'.reverse.map TransvectionStruct.inv, D, _⟩
   suffices
     M =
-      (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod ⬝ (L.map toMatrix).prod ⬝ M ⬝
-        ((L'.map toMatrix).prod ⬝ (L'.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod)
+      (L.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod * (L.map toMatrix).prod * M *
+        ((L'.map toMatrix).prod * (L'.reverse.map (toMatrix ∘ TransvectionStruct.inv)).prod)
     by simpa [← h, Matrix.mul_assoc]
   rw [reverse_inv_prod_mul_prod, prod_mul_reverse_inv_prod, Matrix.one_mul, Matrix.mul_one]
 #align matrix.pivot.exists_list_transvec_mul_diagonal_mul_list_transvec Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec
@@ -704,13 +704,13 @@ assume that the diagonal matrices we consider have the same determinant as `M`.
 obtain similar principles for `SLₙ` or `GLₙ`. -/
 theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matrix n n 𝕜)
     (hdiag : ∀ D : n → 𝕜, det (diagonal D) = det M → P (diagonal D))
-    (htransvec : ∀ t : TransvectionStruct n 𝕜, P t.toMatrix) (hmul : ∀ A B, P A → P B → P (A ⬝ B)) :
+    (htransvec : ∀ t : TransvectionStruct n 𝕜, P t.toMatrix) (hmul : ∀ A B, P A → P B → P (A * B)) :
     P M := by
   rcases exists_list_transvec_mul_diagonal_mul_list_transvec M with ⟨L, L', D, h⟩
   have PD : P (diagonal D) := hdiag D (by simp [h])
   suffices H :
     ∀ (L₁ L₂ : List (TransvectionStruct n 𝕜)) (E : Matrix n n 𝕜),
-      P E → P ((L₁.map toMatrix).prod ⬝ E ⬝ (L₂.map toMatrix).prod)
+      P E → P ((L₁.map toMatrix).prod * E * (L₂.map toMatrix).prod)
   · rw [h]
     apply H L L'
     exact PD
@@ -719,10 +719,10 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
   · simp only [Matrix.one_mul, List.prod_nil, List.map]
     induction' L₂ with t L₂ IH generalizing E
     · simpa
-    · simp only [← Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map]
+    · simp only [← Matrix.mul_assoc, List.prod_cons, List.map]
       apply IH
       exact hmul _ _ PE (htransvec _)
-  · simp only [Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map] at IH ⊢
+  · simp only [Matrix.mul_assoc, List.prod_cons, List.map] at IH ⊢
     exact hmul _ _ (htransvec _) IH
 #align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_induction
 
@@ -733,7 +733,7 @@ invertible matrices are generated by invertible diagonal matrices and transvecti
 theorem diagonal_transvection_induction_of_det_ne_zero (P : Matrix n n 𝕜 → Prop) (M : Matrix n n 𝕜)
     (hMdet : det M ≠ 0) (hdiag : ∀ D : n → 𝕜, det (diagonal D) ≠ 0 → P (diagonal D))
     (htransvec : ∀ t : TransvectionStruct n 𝕜, P t.toMatrix)
-    (hmul : ∀ A B, det A ≠ 0 → det B ≠ 0 → P A → P B → P (A ⬝ B)) : P M := by
+    (hmul : ∀ A B, det A ≠ 0 → det B ≠ 0 → P A → P B → P (A * B)) : P M := by
   let Q : Matrix n n 𝕜 → Prop := fun N => det N ≠ 0 ∧ P N
   have : Q M := by
     apply diagonal_transvection_induction Q M

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

This has nice performance benefits.

@@ -67,7 +67,7 @@ namespace Matrix
 
 open Matrix
 
-variable (n p : Type _) (R : Type u₂) {𝕜 : Type _} [Field 𝕜]
+variable (n p : Type*) (R : Type u₂) {𝕜 : Type*} [Field 𝕜]
 
 variable [DecidableEq n] [DecidableEq p]
 

@@ -16,7 +16,7 @@ import Mathlib.Tactic.FieldSimp
 
 Transvections are matrices of the form `1 + StdBasisMatrix i j c`, where `StdBasisMatrix i j c`
 is the basic matrix with a `c` at position `(i, j)`. Multiplying by such a transvection on the left
-(resp. on the right) amounts to adding `c` times the `j`-th row to to the `i`-th row
+(resp. on the right) amounts to adding `c` times the `j`-th row to the `i`-th row
 (resp `c` times the `i`-th column to the `j`-th column). Therefore, they are useful to present
 algorithms operating on rows and columns.
 

• 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) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.transvection
-! leanprover-community/mathlib commit 0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Matrix.Basis
 import Mathlib.Data.Matrix.DMatrix
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.Matrix.Determinant
 import Mathlib.LinearAlgebra.Matrix.Reindex
 import Mathlib.Tactic.FieldSimp
 
+#align_import linear_algebra.matrix.transvection from "leanprover-community/mathlib"@"0e2aab2b0d521f060f62a14d2cf2e2c54e8491d6"
+
 /-!
 # Transvections
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -565,7 +565,7 @@ theorem exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec
   -- when the last coefficient is zero but there is a nonzero coefficient on the last row or the
   -- last column, we will first put this nonzero coefficient in last position, and then argue as
   -- above.
-  push_neg  at hM
+  push_neg at hM
   simp only [not_and_or, IsTwoBlockDiagonal, toBlocks₁₂, toBlocks₂₁, ← Matrix.ext_iff] at H
   have : ∃ i : Fin r, M (inl i) (inr unit) ≠ 0 ∨ M (inr unit) (inl i) ≠ 0 := by
     cases' H with H H
@@ -725,7 +725,7 @@ theorem diagonal_transvection_induction (P : Matrix n n 𝕜 → Prop) (M : Matr
     · simp only [← Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map]
       apply IH
       exact hmul _ _ PE (htransvec _)
-  · simp only [Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map] at IH⊢
+  · simp only [Matrix.mul_assoc, List.prod_cons, mul_eq_mul, List.map] at IH ⊢
     exact hmul _ _ (htransvec _) IH
 #align matrix.diagonal_transvection_induction Matrix.diagonal_transvection_induction
 

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

@@ -100,7 +100,7 @@ theorem updateRow_eq_transvection [Finite n] (c : R) :
     updateRow (1 : Matrix n n R) i ((1 : Matrix n n R) i + c • (1 : Matrix n n R) j) =
       transvection i j c := by
   cases nonempty_fintype n
-  ext (a b)
+  ext a b
   by_cases ha : i = a; by_cases hb : j = b
   · simp only [updateRow_self, transvection, ha, hb, Pi.add_apply, StdBasisMatrix.apply_same,
       one_apply_eq, Pi.smul_apply, mul_one, Algebra.id.smul_eq_mul, add_apply]
@@ -255,7 +255,7 @@ def sumInl (t : TransvectionStruct n R) : TransvectionStruct (Sum n p) R where
 theorem toMatrix_sumInl (t : TransvectionStruct n R) :
     (t.sumInl p).toMatrix = fromBlocks t.toMatrix 0 0 1 := by
   cases t
-  ext (a b)
+  ext a b
   cases' a with a a <;> cases' b with b b
   · by_cases h : a = b <;> simp [TransvectionStruct.sumInl, transvection, h, stdBasisMatrix]
   · simp [TransvectionStruct.sumInl, transvection]
@@ -299,7 +299,7 @@ variable [Fintype n] [Fintype p]
 theorem toMatrix_reindexEquiv (e : n ≃ p) (t : TransvectionStruct n R) :
     (t.reindexEquiv e).toMatrix = reindexAlgEquiv R e t.toMatrix := by
   rcases t with ⟨t_i, t_j, _⟩
-  ext (a b)
+  ext a b
   simp only [reindexEquiv, transvection, mul_boole, Algebra.id.smul_eq_mul, toMatrix_mk,
     submatrix_apply, reindex_apply, DMatrix.add_apply, Pi.smul_apply, reindexAlgEquiv_apply]
   by_cases ha : e t_i = a <;> by_cases hb : e t_j = b <;> by_cases hab : a = b <;>
@@ -525,10 +525,10 @@ theorem isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
     (hM : M (inr unit) (inr unit) ≠ 0) :
     IsTwoBlockDiagonal ((listTransvecCol M).prod ⬝ M ⬝ (listTransvecRow M).prod) := by
   constructor
-  · ext (i j)
+  · ext i j
     have : j = unit := by simp only [eq_iff_true_of_subsingleton]
     simp [toBlocks₁₂, this, listTransvecCol_mul_mul_listTransvecRow_last_row M hM]
-  · ext (i j)
+  · ext i j
     have : i = unit := by simp only [eq_iff_true_of_subsingleton]
     simp [toBlocks₂₁, this, listTransvecCol_mul_mul_listTransvecRow_last_col M hM]
 #align matrix.pivot.is_two_block_diagonal_list_transvec_col_mul_mul_list_transvec_row Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow
@@ -654,7 +654,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
       (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
   induction' hn : Fintype.card n with r IH generalizing n M
   · refine' ⟨List.nil, List.nil, fun _ => 1, _⟩
-    ext (i j)
+    ext i j
     rw [Fintype.card_eq_zero_iff] at hn
     exact hn.elim' i
   · have e : n ≃ Sum (Fin r) Unit := by

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

@@ -598,10 +598,10 @@ diagonal form by elementary operations, then one deduces it for matrices over `F
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
     (IH :
       ∀ M : Matrix (Fin r) (Fin r) 𝕜,
-        ∃ (L₀ L₀' : List (TransvectionStruct (Fin r) 𝕜))(D₀ : Fin r → 𝕜),
+        ∃ (L₀ L₀' : List (TransvectionStruct (Fin r) 𝕜)) (D₀ : Fin r → 𝕜),
           (L₀.map toMatrix).prod ⬝ M ⬝ (L₀'.map toMatrix).prod = diagonal D₀)
     (M : Matrix (Sum (Fin r) Unit) (Sum (Fin r) Unit) 𝕜) :
-    ∃ (L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜))(D : Sum (Fin r) Unit → 𝕜),
+    ∃ (L L' : List (TransvectionStruct (Sum (Fin r) Unit) 𝕜)) (D : Sum (Fin r) Unit → 𝕜),
       (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
   rcases exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec M with ⟨L₁, L₁', hM⟩
   let M' := (L₁.map toMatrix).prod ⬝ M ⬝ (L₁'.map toMatrix).prod
@@ -628,10 +628,10 @@ variable {n p} [Fintype n] [Fintype p]
 theorem reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix p p 𝕜)
     (e : p ≃ n)
     (H :
-      ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+      ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
         (L.map toMatrix).prod ⬝ Matrix.reindexAlgEquiv 𝕜 e M ⬝ (L'.map toMatrix).prod =
           diagonal D) :
-    ∃ (L L' : List (TransvectionStruct p 𝕜))(D : p → 𝕜),
+    ∃ (L L' : List (TransvectionStruct p 𝕜)) (D : p → 𝕜),
       (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
   rcases H with ⟨L₀, L₀', D₀, h₀⟩
   refine' ⟨L₀.map (reindexEquiv e.symm), L₀'.map (reindexEquiv e.symm), D₀ ∘ e, _⟩
@@ -650,7 +650,7 @@ See `exists_list_transvec_mul_mul_list_transvec_eq_diagonal` for the general ver
 from this one and reindexing). -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [Fintype n]
     [DecidableEq n] (M : Matrix n n 𝕜) :
-    ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+    ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
   induction' hn : Fintype.card n with r IH generalizing n M
   · refine' ⟨List.nil, List.nil, fun _ => 1, _⟩
@@ -670,7 +670,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux (n : Type) [F
 
 /-- Any matrix can be reduced to diagonal form by elementary operations. -/
 theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 𝕜) :
-    ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+    ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       (L.map toMatrix).prod ⬝ M ⬝ (L'.map toMatrix).prod = diagonal D := by
   have e : n ≃ Fin (Fintype.card n) := Fintype.equivOfCardEq (by simp)
   apply reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal M e
@@ -680,7 +680,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal (M : Matrix n n 
 /-- Any matrix can be written as the product of transvections, a diagonal matrix, and
 transvections.-/
 theorem exists_list_transvec_mul_diagonal_mul_list_transvec (M : Matrix n n 𝕜) :
-    ∃ (L L' : List (TransvectionStruct n 𝕜))(D : n → 𝕜),
+    ∃ (L L' : List (TransvectionStruct n 𝕜)) (D : n → 𝕜),
       M = (L.map toMatrix).prod ⬝ diagonal D ⬝ (L'.map toMatrix).prod := by
   rcases exists_list_transvec_mul_mul_list_transvec_eq_diagonal M with ⟨L, L', D, h⟩
   refine' ⟨L.reverse.map TransvectionStruct.inv, L'.reverse.map TransvectionStruct.inv, D, _⟩

These are all doc fixes

@@ -615,7 +615,7 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
       diagonal (Sum.elim D₀ fun _ => c) by
     simpa [Matrix.mul_assoc]
   have : M' = fromBlocks M'' 0 0 (diagonal fun _ => c) := by
-    -- porting note: simplyfied proof, because `congr` didn't work anymore
+    -- porting note: simplified proof, because `congr` didn't work anymore
     rw [← fromBlocks_toBlocks M', hM.1, hM.2]
     rfl
   rw [this]

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -611,11 +611,9 @@ theorem exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction
   refine'
     ⟨L₀.map (sumInl Unit) ++ L₁, L₁' ++ L₀'.map (sumInl Unit),
       Sum.elim D₀ fun _ => M' (inr unit) (inr unit), _⟩
-  suffices
-    (L₀.map (toMatrix ∘ sumInl Unit)).prod ⬝ M' ⬝ (L₀'.map (toMatrix ∘ sumInl Unit)).prod =
-      diagonal (Sum.elim D₀ fun _ => c)
-    by
-      simpa [Matrix.mul_assoc]
+  suffices (L₀.map (toMatrix ∘ sumInl Unit)).prod ⬝ M' ⬝ (L₀'.map (toMatrix ∘ sumInl Unit)).prod =
+      diagonal (Sum.elim D₀ fun _ => c) by
+    simpa [Matrix.mul_assoc]
   have : M' = fromBlocks M'' 0 0 (diagonal fun _ => c) := by
     -- porting note: simplyfied proof, because `congr` didn't work anymore
     rw [← fromBlocks_toBlocks M', hM.1, hM.2]

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>