linear_algebra.matrix.determinant | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

c3019c79

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

86d1873c

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Chris Hughes, Tim Baanen
 -/
-import Data.Matrix.Pequiv
+import Data.Matrix.PEquiv
 import Data.Matrix.Block
 import Data.Matrix.Notation
 import Data.Fintype.BigOperators
@@ -11,7 +11,7 @@ import GroupTheory.Perm.Fin
 import GroupTheory.Perm.Sign
 import Algebra.Algebra.Basic
 import Tactic.Ring
-import LinearAlgebra.Alternating
+import LinearAlgebra.Alternating.Basic
 import LinearAlgebra.Pi
 
 #align_import linear_algebra.matrix.determinant from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
@@ -850,7 +850,7 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   -- `perm (fin n.succ)` than the determinant of the submatrix we want,
   -- permute `A` so that we get the correct one.
   have : (-1 : R) ^ (i : ℕ) = i.cycle_range.sign := by simp [Fin.sign_cycleRange]
-  rw [Fin.val_succ, pow_succ, this, mul_assoc, mul_assoc, mul_left_comm ↑(Equiv.Perm.sign _), ←
+  rw [Fin.val_succ, pow_succ', this, mul_assoc, mul_assoc, mul_left_comm ↑(Equiv.Perm.sign _), ←
     det_permute, Matrix.det_apply, Finset.mul_sum, Finset.mul_sum]
   -- now we just need to move the corresponding parts to the same place
   refine' Finset.sum_congr rfl fun σ _ => _

86d1873c

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -166,8 +166,8 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
   by
   obtain ⟨i, j, hpij, hij⟩ : ∃ i j, p i = p j ∧ i ≠ j :=
     by
-    rw [← Finite.injective_iff_bijective, injective] at H 
-    push_neg at H 
+    rw [← Finite.injective_iff_bijective, injective] at H
+    push_neg at H
     exact H
   exact
     sum_involution (fun σ _ => σ * swap i j)
@@ -644,7 +644,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   have M_k : M k.cast_succ = M' k.cast_succ := (update_row_ne k_ne_succ).symm
   rw [hM, M_k, det_update_row_add_smul_self M' k_ne_succ.symm, ih (Function.update c k 0)]
   · intro i hi
-    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi 
+    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi
     rw [Function.update_apply]
     split_ifs with hik; · rfl
     exact hc _ (fin.succ_lt_succ_iff.mpr (lt_of_le_of_ne hi (Ne.symm hik)))
@@ -718,16 +718,16 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
       prod_congr_left_apply]
   · intro σ σ' _ _ eq
     ext x hx k
-    simp only at eq 
+    simp only at eq
     have :
       ∀ k x,
         prod_congr_left (fun k => σ k (Finset.mem_univ _)) (k, x) =
           prod_congr_left (fun k => σ' k (Finset.mem_univ _)) (k, x) :=
       fun k x => by rw [Eq]
-    simp only [prod_congr_left_apply, Prod.mk.inj_iff] at this 
+    simp only [prod_congr_left_apply, Prod.mk.inj_iff] at this
     exact (this k x).1
   · intro σ hσ
-    rw [mem_preserving_snd] at hσ 
+    rw [mem_preserving_snd] at hσ
     have hσ' : ∀ x, (σ⁻¹ x).snd = x.snd := by intro x;
       conv_rhs => rw [← perm.apply_inv_self σ x, hσ]
     have mk_apply_eq : ∀ k x, ((σ (x, k)).fst, k) = σ (x, k) :=
@@ -753,7 +753,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
       · simp only [coe_fn_mk, prod_congr_left_apply]
       · simp only [prod_congr_left_apply, hσ]
   · intro σ _ hσ
-    rw [mem_preserving_snd] at hσ 
+    rw [mem_preserving_snd] at hσ
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
     rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), MulZeroClass.mul_zero]
     rw [← @Prod.mk.eta _ _ (σ (k, x)), block_diagonal_apply_ne]
@@ -793,12 +793,12 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     intro h
     have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
       exact congr_fun (congr_arg to_fun h) x
-    simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2 
+    simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2
     ext
     · exact h2.left x
     · exact h2.right x
   · intro σ hσ
-    erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ 
+    erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ
     obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
     use σ₁₂
     rw [← hσ₁₂]
@@ -807,7 +807,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) :=
       by
       by_contra
-      rw [Set.mem_toFinset] at hσn 
+      rw [Set.mem_toFinset] at hσn
       apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
       rintro x ⟨a, ha⟩
       rw [← ha]; exact h a

86d1873c

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -767,7 +767,56 @@ the determinants of the diagonal blocks. For the generalization to any number of
 `matrix.det_of_upper_triangular`. -/
 @[simp]
 theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Matrix n n R) :
-    (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by classical
+    (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by
+  classical
+  simp_rw [det_apply']
+  convert
+    (sum_subset (subset_univ ((sum_congr_hom m n).range : Set (perm (Sum m n))).toFinset) _).symm
+  rw [sum_mul_sum]
+  simp_rw [univ_product_univ]
+  rw [(sum_bij (fun (σ : perm m × perm n) _ => Equiv.sumCongr σ.fst σ.snd) _ _ _ _).symm]
+  · intro σ₁₂ h
+    simp only
+    erw [Set.mem_toFinset, MonoidHom.mem_range]
+    use σ₁₂
+    simp only [sum_congr_hom_apply]
+  · simp only [forall_prop_of_true, Prod.forall, mem_univ]
+    intro σ₁ σ₂
+    rw [Fintype.prod_sum_type]
+    simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, from_blocks_apply₁₁,
+      from_blocks_apply₂₂]
+    rw [mul_mul_mul_comm]
+    congr
+    rw [sign_sum_congr, Units.val_mul, Int.cast_mul]
+  · intro σ₁ σ₂ h₁ h₂
+    dsimp only
+    intro h
+    have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
+      exact congr_fun (congr_arg to_fun h) x
+    simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2 
+    ext
+    · exact h2.left x
+    · exact h2.right x
+  · intro σ hσ
+    erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ 
+    obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
+    use σ₁₂
+    rw [← hσ₁₂]
+    simp
+  · intro σ hσ hσn
+    have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) :=
+      by
+      by_contra
+      rw [Set.mem_toFinset] at hσn 
+      apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
+      rintro x ⟨a, ha⟩
+      rw [← ha]; exact h a
+    obtain ⟨a, ha⟩ := not_forall.mp h1
+    cases' hx : σ (Sum.inl a) with a2 b
+    · have hn := (not_exists.mp ha) a2
+      exact absurd hx.symm hn
+    · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
+      rw [hx, from_blocks_apply₂₁]; rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
 -/

86d1873c

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -767,56 +767,7 @@ the determinants of the diagonal blocks. For the generalization to any number of
 `matrix.det_of_upper_triangular`. -/
 @[simp]
 theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Matrix n n R) :
-    (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by
-  classical
-  simp_rw [det_apply']
-  convert
-    (sum_subset (subset_univ ((sum_congr_hom m n).range : Set (perm (Sum m n))).toFinset) _).symm
-  rw [sum_mul_sum]
-  simp_rw [univ_product_univ]
-  rw [(sum_bij (fun (σ : perm m × perm n) _ => Equiv.sumCongr σ.fst σ.snd) _ _ _ _).symm]
-  · intro σ₁₂ h
-    simp only
-    erw [Set.mem_toFinset, MonoidHom.mem_range]
-    use σ₁₂
-    simp only [sum_congr_hom_apply]
-  · simp only [forall_prop_of_true, Prod.forall, mem_univ]
-    intro σ₁ σ₂
-    rw [Fintype.prod_sum_type]
-    simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, from_blocks_apply₁₁,
-      from_blocks_apply₂₂]
-    rw [mul_mul_mul_comm]
-    congr
-    rw [sign_sum_congr, Units.val_mul, Int.cast_mul]
-  · intro σ₁ σ₂ h₁ h₂
-    dsimp only
-    intro h
-    have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
-      exact congr_fun (congr_arg to_fun h) x
-    simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2 
-    ext
-    · exact h2.left x
-    · exact h2.right x
-  · intro σ hσ
-    erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ 
-    obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
-    use σ₁₂
-    rw [← hσ₁₂]
-    simp
-  · intro σ hσ hσn
-    have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) :=
-      by
-      by_contra
-      rw [Set.mem_toFinset] at hσn 
-      apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
-      rintro x ⟨a, ha⟩
-      rw [← ha]; exact h a
-    obtain ⟨a, ha⟩ := not_forall.mp h1
-    cases' hx : σ (Sum.inl a) with a2 b
-    · have hn := (not_exists.mp ha) a2
-      exact absurd hx.symm hn
-    · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
-      rw [hx, from_blocks_apply₂₁]; rfl
+    (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by classical
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
 -/

86d1873c

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -92,7 +92,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   rw [det_apply']
   refine' (Finset.sum_eq_single 1 _ _).trans _
   · intro σ h1 h2
-    cases' not_forall.1 (mt Equiv.ext h2) with x h3
+    cases' Classical.not_forall.1 (mt Equiv.ext h2) with x h3
     convert MulZeroClass.mul_zero _
     apply Finset.prod_eq_zero
     · change x ∈ _; simp

86d1873c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,16 +3,16 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Chris Hughes, Tim Baanen
 -/
-import Mathbin.Data.Matrix.Pequiv
-import Mathbin.Data.Matrix.Block
-import Mathbin.Data.Matrix.Notation
-import Mathbin.Data.Fintype.BigOperators
-import Mathbin.GroupTheory.Perm.Fin
-import Mathbin.GroupTheory.Perm.Sign
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Tactic.Ring
-import Mathbin.LinearAlgebra.Alternating
-import Mathbin.LinearAlgebra.Pi
+import Data.Matrix.Pequiv
+import Data.Matrix.Block
+import Data.Matrix.Notation
+import Data.Fintype.BigOperators
+import GroupTheory.Perm.Fin
+import GroupTheory.Perm.Sign
+import Algebra.Algebra.Basic
+import Tactic.Ring
+import LinearAlgebra.Alternating
+import LinearAlgebra.Pi
 
 #align_import linear_algebra.matrix.determinant from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"

86d1873c

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -332,7 +332,7 @@ theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matri
 #print Matrix.det_smul /-
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
-    det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
+    det (c • A) = det (HMul.hMul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
     _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
 #align matrix.det_smul Matrix.det_smul

86d1873c

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Chris Hughes, Tim Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.determinant
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Matrix.Pequiv
 import Mathbin.Data.Matrix.Block
@@ -19,6 +14,8 @@ import Mathbin.Tactic.Ring
 import Mathbin.LinearAlgebra.Alternating
 import Mathbin.LinearAlgebra.Pi
 
+#align_import linear_algebra.matrix.determinant from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 # Determinant of a matrix

86d1873c

bump to nightly-2023-07-16-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

6db63fa6

Diff

@@ -643,11 +643,11 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     by_cases hi : i = k.succ
     · simp [hi, hM', hsucc, update_row_self]
     rw [update_row_ne hi, hM', update_row_ne hi]
-  have k_ne_succ : k.cast_succ ≠ k.succ := (Fin.castSuccEmb_lt_succ k).Ne
+  have k_ne_succ : k.cast_succ ≠ k.succ := (Fin.castSucc_lt_succ k).Ne
   have M_k : M k.cast_succ = M' k.cast_succ := (update_row_ne k_ne_succ).symm
   rw [hM, M_k, det_update_row_add_smul_self M' k_ne_succ.symm, ih (Function.update c k 0)]
   · intro i hi
-    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff] at hi 
+    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi 
     rw [Function.update_apply]
     split_ifs with hik; · rfl
     exact hc _ (fin.succ_lt_succ_iff.mpr (lt_of_le_of_ne hi (Ne.symm hik)))
@@ -661,7 +661,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · simp [hc i (fin.succ_lt_succ_iff.mpr hik2)]
   rw [update_row_ne]
   apply ne_of_lt
-  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
+  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 -/
 
@@ -838,7 +838,7 @@ theorem det_fromBlocks_zero₁₂ (A : Matrix m m R) (C : Matrix n m R) (D : Mat
 #print Matrix.det_succ_column_zero /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along column 0. -/
 theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) :
-    det A = ∑ i : Fin n.succ, (-1) ^ (i : ℕ) * A i 0 * det (A.submatrix i.succAbove Fin.succ) :=
+    det A = ∑ i : Fin n.succ, (-1) ^ (i : ℕ) * A i 0 * det (A.submatrix i.succAboveEmb Fin.succ) :=
   by
   rw [Matrix.det_apply, Finset.univ_perm_fin_succ, ← Finset.univ_product_univ]
   simp only [Finset.sum_map, Equiv.toEmbedding_apply, Finset.sum_product, Matrix.submatrix]
@@ -861,14 +861,15 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   calc
     (-1 * σ.sign : ℤ) • ∏ i', A (equiv.perm.decompose_fin.symm (Fin.succ i, σ) i') i' =
         (-1 * σ.sign : ℤ) •
-          (A (Fin.succ i) 0 * ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) :=
+          (A (Fin.succ i) 0 *
+            ∏ i', A ((Fin.succ i).succAboveEmb (Fin.cycleRange i (σ i'))) i'.succ) :=
       by
       simp only [Fin.prod_univ_succ, Fin.succAbove_cycleRange,
         Equiv.Perm.decomposeFin_symm_apply_zero, Equiv.Perm.decomposeFin_symm_apply_succ]
     _ =
         -1 *
           (A (Fin.succ i) 0 *
-            (σ.sign : ℤ) • ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) :=
+            (σ.sign : ℤ) • ∏ i', A ((Fin.succ i).succAboveEmb (Fin.cycleRange i (σ i'))) i'.succ) :=
       by
       simp only [mul_assoc, mul_comm, _root_.neg_mul, one_mul, zsmul_eq_mul, neg_inj, neg_smul,
         Fin.succAbove_cycleRange]
@@ -878,7 +879,7 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
 #print Matrix.det_succ_row_zero /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along row 0. -/
 theorem det_succ_row_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) :
-    det A = ∑ j : Fin n.succ, (-1) ^ (j : ℕ) * A 0 j * det (A.submatrix Fin.succ j.succAbove) :=
+    det A = ∑ j : Fin n.succ, (-1) ^ (j : ℕ) * A 0 j * det (A.submatrix Fin.succ j.succAboveEmb) :=
   by
   rw [← det_transpose A, det_succ_column_zero]
   refine' Finset.sum_congr rfl fun i _ => _
@@ -891,7 +892,8 @@ theorem det_succ_row_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) :
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along row `i`. -/
 theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin n.succ) :
     det A =
-      ∑ j : Fin n.succ, (-1) ^ (i + j : ℕ) * A i j * det (A.submatrix i.succAbove j.succAbove) :=
+      ∑ j : Fin n.succ,
+        (-1) ^ (i + j : ℕ) * A i j * det (A.submatrix i.succAboveEmb j.succAboveEmb) :=
   by
   simp_rw [pow_add, mul_assoc, ← mul_sum]
   have : det A = (-1 : R) ^ (i : ℕ) * i.cycle_range⁻¹.sign * det A := by
@@ -914,7 +916,8 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along column `j`. -/
 theorem det_succ_column {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (j : Fin n.succ) :
     det A =
-      ∑ i : Fin n.succ, (-1) ^ (i + j : ℕ) * A i j * det (A.submatrix i.succAbove j.succAbove) :=
+      ∑ i : Fin n.succ,
+        (-1) ^ (i + j : ℕ) * A i j * det (A.submatrix i.succAboveEmb j.succAboveEmb) :=
   by
   rw [← det_transpose, det_succ_row _ j]
   refine' Finset.sum_congr rfl fun i _ => _

86d1873c

bump to nightly-2023-07-06-11

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

a2f50eda

Diff

@@ -643,11 +643,11 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     by_cases hi : i = k.succ
     · simp [hi, hM', hsucc, update_row_self]
     rw [update_row_ne hi, hM', update_row_ne hi]
-  have k_ne_succ : k.cast_succ ≠ k.succ := (Fin.castSucc_lt_succ k).Ne
+  have k_ne_succ : k.cast_succ ≠ k.succ := (Fin.castSuccEmb_lt_succ k).Ne
   have M_k : M k.cast_succ = M' k.cast_succ := (update_row_ne k_ne_succ).symm
   rw [hM, M_k, det_update_row_add_smul_self M' k_ne_succ.symm, ih (Function.update c k 0)]
   · intro i hi
-    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi 
+    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff] at hi 
     rw [Function.update_apply]
     split_ifs with hik; · rfl
     exact hc _ (fin.succ_lt_succ_iff.mpr (lt_of_le_of_ne hi (Ne.symm hik)))
@@ -661,7 +661,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · simp [hc i (fin.succ_lt_succ_iff.mpr hik2)]
   rw [update_row_ne]
   apply ne_of_lt
-  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
+  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 -/

86d1873c

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -593,7 +593,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       contrapose! hs
       simp [hs]
     congr
-    ext (i j)
+    ext i j
     rw [A_eq, this, MulZeroClass.zero_mul, add_zero]
   · intro i s hi ih B c hs k hk A_eq
     have hAi : A i = B i + c i • B k := funext (A_eq i)
@@ -633,13 +633,13 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   by
   refine' Fin.induction _ (fun k ih => _) k <;> intro c hc M N h0 hsucc
   · congr
-    ext (i j)
+    ext i j
     refine' Fin.cases (h0 j) (fun i => _) i
     rw [hsucc, hc i (Fin.succ_pos _), MulZeroClass.zero_mul, add_zero]
   set M' := update_row M k.succ (N k.succ) with hM'
   have hM : M = update_row M' k.succ (M' k.succ + c k • M k.cast_succ) :=
     by
-    ext (i j)
+    ext i j
     by_cases hi : i = k.succ
     · simp [hi, hM', hsucc, update_row_self]
     rw [update_row_ne hi, hM', update_row_ne hi]
@@ -720,7 +720,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
     simp only [sign_prod_congr_left, Units.coe_prod, Int.cast_prod, block_diagonal_apply_eq,
       prod_congr_left_apply]
   · intro σ σ' _ _ eq
-    ext (x hx k)
+    ext x hx k
     simp only at eq 
     have :
       ∀ k x,
@@ -905,7 +905,7 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
   rw [mul_assoc, Matrix.submatrix, Matrix.submatrix]
   congr
   · rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_zero]
-  · ext (i' j')
+  · ext i' j'
     rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_succ]
 #align matrix.det_succ_row Matrix.det_succ_row
 -/

86d1873c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -59,7 +59,6 @@ variable {m n : Type _} [DecidableEq n] [Fintype n] [DecidableEq m] [Fintype m]
 
 variable {R : Type v} [CommRing R]
 
--- mathport name: «exprε »
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
 #print Matrix.detRowAlternating /-
@@ -76,15 +75,20 @@ abbrev det (M : Matrix n n R) : R :=
 #align matrix.det Matrix.det
 -/
 
+#print Matrix.det_apply /-
 theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, σ.sign • ∏ i, M (σ i) i :=
   MultilinearMap.alternatization_apply _ M
 #align matrix.det_apply Matrix.det_apply
+-/
 
+#print Matrix.det_apply' /-
 -- This is what the old definition was. We use it to avoid having to change the old proofs below
 theorem det_apply' (M : Matrix n n R) : M.det = ∑ σ : Perm n, ε σ * ∏ i, M (σ i) i := by
   simp [det_apply, Units.smul_def]
 #align matrix.det_apply' Matrix.det_apply'
+-/
 
+#print Matrix.det_diagonal /-
 @[simp]
 theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   by
@@ -99,29 +103,41 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   · simp
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
+-/
 
+#print Matrix.det_zero /-
 @[simp]
 theorem det_zero (h : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
 #align matrix.det_zero Matrix.det_zero
+-/
 
+#print Matrix.det_one /-
 @[simp]
 theorem det_one : det (1 : Matrix n n R) = 1 := by rw [← diagonal_one] <;> simp [-diagonal_one]
 #align matrix.det_one Matrix.det_one
+-/
 
+#print Matrix.det_isEmpty /-
 theorem det_isEmpty [IsEmpty n] {A : Matrix n n R} : det A = 1 := by simp [det_apply]
 #align matrix.det_is_empty Matrix.det_isEmpty
+-/
 
+#print Matrix.coe_det_isEmpty /-
 @[simp]
 theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.const _ 1 := by ext;
   exact det_is_empty
 #align matrix.coe_det_is_empty Matrix.coe_det_isEmpty
+-/
 
+#print Matrix.det_eq_one_of_card_eq_zero /-
 theorem det_eq_one_of_card_eq_zero {A : Matrix n n R} (h : Fintype.card n = 0) : det A = 1 :=
   haveI : IsEmpty n := fintype.card_eq_zero_iff.mp h
   det_is_empty
 #align matrix.det_eq_one_of_card_eq_zero Matrix.det_eq_one_of_card_eq_zero
+-/
 
+#print Matrix.det_unique /-
 /-- If `n` has only one element, the determinant of an `n` by `n` matrix is just that element.
 Although `unique` implies `decidable_eq` and `fintype`, the instances might
 not be syntactically equal. Thus, we need to fill in the args explicitly. -/
@@ -129,19 +145,25 @@ not be syntactically equal. Thus, we need to fill in the args explicitly. -/
 theorem det_unique {n : Type _} [Unique n] [DecidableEq n] [Fintype n] (A : Matrix n n R) :
     det A = A default default := by simp [det_apply, univ_unique]
 #align matrix.det_unique Matrix.det_unique
+-/
 
+#print Matrix.det_eq_elem_of_subsingleton /-
 theorem det_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) : det A = A k k :=
   by
   convert det_unique _
   exact uniqueOfSubsingleton k
 #align matrix.det_eq_elem_of_subsingleton Matrix.det_eq_elem_of_subsingleton
+-/
 
+#print Matrix.det_eq_elem_of_card_eq_one /-
 theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (k : n) :
     det A = A k k :=
   haveI : Subsingleton n := fintype.card_le_one_iff_subsingleton.mp h.le
   det_eq_elem_of_subsingleton _ _
 #align matrix.det_eq_elem_of_card_eq_one Matrix.det_eq_elem_of_card_eq_one
+-/
 
+#print Matrix.det_mul_aux /-
 theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     ∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x = 0 :=
   by
@@ -160,7 +182,9 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
       (fun σ _ _ => (not_congr mul_swap_eq_iff).mpr hij) (fun _ _ => mem_univ _) fun σ _ =>
       mul_swap_involutive i j σ
 #align matrix.det_mul_aux Matrix.det_mul_aux
+-/
 
+#print Matrix.det_mul /-
 @[simp]
 theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
   calc
@@ -194,6 +218,7 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
           simp only [this])
     _ = det M * det N := by simp only [det_apply', Finset.mul_sum, mul_comm, mul_left_comm]
 #align matrix.det_mul Matrix.det_mul
+-/
 
 #print Matrix.detMonoidHom /-
 /-- The determinant of a matrix, as a monoid homomorphism. -/
@@ -204,36 +229,49 @@ def detMonoidHom : Matrix n n R →* R where
 #align matrix.det_monoid_hom Matrix.detMonoidHom
 -/
 
+#print Matrix.coe_detMonoidHom /-
 @[simp]
 theorem coe_detMonoidHom : (detMonoidHom : Matrix n n R → R) = det :=
   rfl
 #align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHom
+-/
 
+#print Matrix.det_mul_comm /-
 /-- On square matrices, `mul_comm` applies under `det`. -/
 theorem det_mul_comm (M N : Matrix m m R) : det (M ⬝ N) = det (N ⬝ M) := by
   rw [det_mul, det_mul, mul_comm]
 #align matrix.det_mul_comm Matrix.det_mul_comm
+-/
 
+#print Matrix.det_mul_left_comm /-
 /-- On square matrices, `mul_left_comm` applies under `det`. -/
 theorem det_mul_left_comm (M N P : Matrix m m R) : det (M ⬝ (N ⬝ P)) = det (N ⬝ (M ⬝ P)) := by
   rw [← Matrix.mul_assoc, ← Matrix.mul_assoc, det_mul, det_mul_comm M N, ← det_mul]
 #align matrix.det_mul_left_comm Matrix.det_mul_left_comm
+-/
 
+#print Matrix.det_mul_right_comm /-
 /-- On square matrices, `mul_right_comm` applies under `det`. -/
 theorem det_mul_right_comm (M N P : Matrix m m R) : det (M ⬝ N ⬝ P) = det (M ⬝ P ⬝ N) := by
   rw [Matrix.mul_assoc, Matrix.mul_assoc, det_mul, det_mul_comm N P, ← det_mul]
 #align matrix.det_mul_right_comm Matrix.det_mul_right_comm
+-/
 
+#print Matrix.det_units_conj /-
 theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M ⬝ N ⬝ ↑M⁻¹ : Matrix m m R) = det N := by
   rw [det_mul_right_comm, ← mul_eq_mul, ← mul_eq_mul, Units.mul_inv, one_mul]
 #align matrix.det_units_conj Matrix.det_units_conj
+-/
 
+#print Matrix.det_units_conj' /-
 theorem det_units_conj' (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M⁻¹ ⬝ N ⬝ ↑M : Matrix m m R) = det N :=
   det_units_conj M⁻¹ N
 #align matrix.det_units_conj' Matrix.det_units_conj'
+-/
 
+#print Matrix.det_transpose /-
 /-- Transposing a matrix preserves the determinant. -/
 @[simp]
 theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
@@ -247,13 +285,17 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
   intros
   simp
 #align matrix.det_transpose Matrix.det_transpose
+-/
 
+#print Matrix.det_permute /-
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = σ.sign * M.det :=
   ((detRowAlternating : AlternatingMap R (n → R) R n).map_perm M σ).trans (by simp [Units.smul_def])
 #align matrix.det_permute Matrix.det_permute
+-/
 
+#print Matrix.det_submatrix_equiv_self /-
 /-- Permuting rows and columns with the same equivalence has no effect. -/
 @[simp]
 theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.submatrix e e) = det A :=
@@ -267,7 +309,9 @@ theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.subma
   intro i
   rw [Equiv.permCongr_apply, Equiv.symm_apply_apply, submatrix_apply]
 #align matrix.det_submatrix_equiv_self Matrix.det_submatrix_equiv_self
+-/
 
+#print Matrix.det_reindex_self /-
 /-- Reindexing both indices along the same equivalence preserves the determinant.
 
 For the `simp` version of this lemma, see `det_submatrix_equiv_self`; this one is unsuitable because
@@ -276,7 +320,9 @@ For the `simp` version of this lemma, see `det_submatrix_equiv_self`; this one i
 theorem det_reindex_self (e : m ≃ n) (A : Matrix m m R) : det (reindex e e A) = det A :=
   det_submatrix_equiv_self e.symm A
 #align matrix.det_reindex_self Matrix.det_reindex_self
+-/
 
+#print Matrix.det_permutation /-
 /-- The determinant of a permutation matrix equals its sign. -/
 @[simp]
 theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matrix n n R) = σ.sign :=
@@ -284,30 +330,40 @@ theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matri
   rw [← Matrix.mul_one (σ.to_pequiv.to_matrix : Matrix n n R), PEquiv.toPEquiv_mul_matrix,
     det_permute, det_one, mul_one]
 #align matrix.det_permutation Matrix.det_permutation
+-/
 
+#print Matrix.det_smul /-
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
     det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
     _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
 #align matrix.det_smul Matrix.det_smul
+-/
 
+#print Matrix.det_smul_of_tower /-
 @[simp]
 theorem det_smul_of_tower {α} [Monoid α] [DistribMulAction α R] [IsScalarTower α R R]
     [SMulCommClass α R R] (c : α) (A : Matrix n n R) : det (c • A) = c ^ Fintype.card n • det A :=
   by rw [← smul_one_smul R c A, det_smul, smul_pow, one_pow, smul_mul_assoc, one_mul]
 #align matrix.det_smul_of_tower Matrix.det_smul_of_tower
+-/
 
+#print Matrix.det_neg /-
 theorem det_neg (A : Matrix n n R) : det (-A) = (-1) ^ Fintype.card n * det A := by
   rw [← det_smul, neg_one_smul]
 #align matrix.det_neg Matrix.det_neg
+-/
 
+#print Matrix.det_neg_eq_smul /-
 /-- A variant of `matrix.det_neg` with scalar multiplication by `units ℤ` instead of multiplication
 by `R`. -/
 theorem det_neg_eq_smul (A : Matrix n n R) : det (-A) = (-1 : Units ℤ) ^ Fintype.card n • det A :=
   by rw [← det_smul_of_tower, Units.neg_smul, one_smul]
 #align matrix.det_neg_eq_smul Matrix.det_neg_eq_smul
+-/
 
+#print Matrix.det_mul_row /-
 /-- Multiplying each row by a fixed `v i` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_row (v : n → R) (A : Matrix n n R) :
@@ -317,47 +373,62 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
       congr_arg det <| by ext; simp [mul_comm]
     _ = (∏ i, v i) * det A := by rw [det_mul, det_diagonal, mul_comm]
 #align matrix.det_mul_row Matrix.det_mul_row
+-/
 
+#print Matrix.det_mul_column /-
 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_column (v : n → R) (A : Matrix n n R) :
     det (of fun i j => v i * A i j) = (∏ i, v i) * det A :=
   MultilinearMap.map_smul_univ _ v A
 #align matrix.det_mul_column Matrix.det_mul_column
+-/
 
+#print Matrix.det_pow /-
 @[simp]
 theorem det_pow (M : Matrix m m R) (n : ℕ) : det (M ^ n) = det M ^ n :=
   (detMonoidHom : Matrix m m R →* R).map_pow M n
 #align matrix.det_pow Matrix.det_pow
+-/
 
 section HomMap
 
 variable {S : Type w} [CommRing S]
 
+#print RingHom.map_det /-
 theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
 #align ring_hom.map_det RingHom.map_det
+-/
 
+#print RingEquiv.map_det /-
 theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align ring_equiv.map_det RingEquiv.map_det
+-/
 
+#print AlgHom.map_det /-
 theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S →ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align alg_hom.map_det AlgHom.map_det
+-/
 
+#print AlgEquiv.map_det /-
 theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S ≃ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toAlgHom.map_det _
 #align alg_equiv.map_det AlgEquiv.map_det
+-/
 
 end HomMap
 
+#print Matrix.det_conjTranspose /-
 @[simp]
 theorem det_conjTranspose [StarRing R] (M : Matrix m m R) : det Mᴴ = star (det M) :=
   ((starRingEnd R).map_det _).symm.trans <| congr_arg star M.det_transpose
 #align matrix.det_conj_transpose Matrix.det_conjTranspose
+-/
 
 section DetZero
 
@@ -368,63 +439,83 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 -/
 
 
+#print Matrix.det_eq_zero_of_row_eq_zero /-
 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
+-/
 
+#print Matrix.det_eq_zero_of_column_eq_zero /-
 theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) : det A = 0 :=
   by rw [← det_transpose]; exact det_eq_zero_of_row_eq_zero j h
 #align matrix.det_eq_zero_of_column_eq_zero Matrix.det_eq_zero_of_column_eq_zero
+-/
 
 variable {M : Matrix n n R} {i j : n}
 
+#print Matrix.det_zero_of_row_eq /-
 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_eq_zero_of_eq M hij i_ne_j
 #align matrix.det_zero_of_row_eq Matrix.det_zero_of_row_eq
+-/
 
+#print Matrix.det_zero_of_column_eq /-
 /-- If a matrix has a repeated column, the determinant will be zero. -/
 theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) : M.det = 0 := by
   rw [← det_transpose, det_zero_of_row_eq i_ne_j]; exact funext hij
 #align matrix.det_zero_of_column_eq Matrix.det_zero_of_column_eq
+-/
 
 end DetZero
 
+#print Matrix.det_updateRow_add /-
 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_add M j u v
 #align matrix.det_update_row_add Matrix.det_updateRow_add
+-/
 
+#print Matrix.det_updateColumn_add /-
 theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateColumn M j <| u + v) = det (updateColumn M j u) + det (updateColumn M j v) :=
   by
   rw [← det_transpose, ← update_row_transpose, det_update_row_add]
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_add Matrix.det_updateColumn_add
+-/
 
+#print Matrix.det_updateRow_smul /-
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_smul M j s u
 #align matrix.det_update_row_smul Matrix.det_updateRow_smul
+-/
 
+#print Matrix.det_updateColumn_smul /-
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=
   by
   rw [← det_transpose, ← update_row_transpose, det_update_row_smul]
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_smul Matrix.det_updateColumn_smul
+-/
 
+#print Matrix.det_updateRow_smul' /-
 theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateRow M j u) :=
   MultilinearMap.map_update_smul _ M j s u
 #align matrix.det_update_row_smul' Matrix.det_updateRow_smul'
+-/
 
+#print Matrix.det_updateColumn_smul' /-
 theorem det_updateColumn_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateColumn M j u) :=
   by
   rw [← det_transpose, ← update_row_transpose, transpose_smul, det_update_row_smul']
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_smul' Matrix.det_updateColumn_smul'
+-/
 
 section DetEq
 
@@ -434,6 +525,7 @@ Lemmas showing the determinant is invariant under a variety of operations.
 -/
 
 
+#print Matrix.det_eq_of_eq_mul_det_one /-
 theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = B ⬝ C) : det A = det B :=
   calc
@@ -441,7 +533,9 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     _ = det B * det C := (det_mul _ _)
     _ = det B := by rw [hC, mul_one]
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
+-/
 
+#print Matrix.det_eq_of_eq_det_one_mul /-
 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = C ⬝ B) : det A = det B :=
   calc
@@ -449,33 +543,43 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     _ = det C * det B := (det_mul _ _)
     _ = det B := by rw [hC, one_mul]
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul
+-/
 
+#print Matrix.det_updateRow_add_self /-
 theorem det_updateRow_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
     det (updateRow A i (A i + A j)) = det A := by
   simp [det_update_row_add,
     det_zero_of_row_eq hij (update_row_self.trans (update_row_ne hij.symm).symm)]
 #align matrix.det_update_row_add_self Matrix.det_updateRow_add_self
+-/
 
+#print Matrix.det_updateColumn_add_self /-
 theorem det_updateColumn_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
     det (updateColumn A i fun k => A k i + A k j) = det A :=
   by
   rw [← det_transpose, ← update_row_transpose, ← det_transpose A]
   exact det_update_row_add_self Aᵀ hij
 #align matrix.det_update_column_add_self Matrix.det_updateColumn_add_self
+-/
 
+#print Matrix.det_updateRow_add_smul_self /-
 theorem det_updateRow_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateRow A i (A i + c • A j)) = det A := by
   simp [det_update_row_add, det_update_row_smul,
     det_zero_of_row_eq hij (update_row_self.trans (update_row_ne hij.symm).symm)]
 #align matrix.det_update_row_add_smul_self Matrix.det_updateRow_add_smul_self
+-/
 
+#print Matrix.det_updateColumn_add_smul_self /-
 theorem det_updateColumn_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateColumn A i fun k => A k i + c • A k j) = det A :=
   by
   rw [← det_transpose, ← update_row_transpose, ← det_transpose A]
   exact det_update_row_add_smul_self Aᵀ hij c
 #align matrix.det_update_column_add_smul_self Matrix.det_updateColumn_add_smul_self
+-/
 
+#print Matrix.det_eq_of_forall_row_eq_smul_add_const_aux /-
 theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Finset n} :
     ∀ (c : n → R) (hs : ∀ i, i ∉ s → c i = 0) (k : n) (hk : k ∉ s)
       (A_eq : ∀ i j, A i j = B i j + c i * B k j), det A = det B :=
@@ -506,7 +610,9 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       · simp [hi'i]
       rw [A_eq, update_row_ne fun h : k = i => hk <| h ▸ Finset.mem_insert_self k s]
 #align matrix.det_eq_of_forall_row_eq_smul_add_const_aux Matrix.det_eq_of_forall_row_eq_smul_add_const_aux
+-/
 
+#print Matrix.det_eq_of_forall_row_eq_smul_add_const /-
 /-- If you add multiples of row `B k` to other rows, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R) (k : n)
     (hk : c k = 0) (A_eq : ∀ i j, A i j = B i j + c i * B k j) : det A = det B :=
@@ -517,7 +623,9 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
           ⟨mt (fun h : i = k => show c i = 0 from h.symm ▸ hk) hi, Finset.mem_univ i⟩)
     k (Finset.not_mem_erase k Finset.univ) A_eq
 #align matrix.det_eq_of_forall_row_eq_smul_add_const Matrix.det_eq_of_forall_row_eq_smul_add_const
+-/
 
+#print Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux /-
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (hc : ∀ i : Fin n, k < i.succ → c i = 0)
       {M N : Matrix (Fin n.succ) (Fin n.succ) R} (h0 : ∀ j, M 0 j = N 0 j)
@@ -555,7 +663,9 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   apply ne_of_lt
   rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
+-/
 
+#print Matrix.det_eq_of_forall_row_eq_smul_add_pred /-
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ j, A 0 j = B 0 j)
@@ -563,7 +673,9 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
   det_eq_of_forall_row_eq_smul_add_pred_aux (Fin.last _) c
     (fun i hi => absurd hi (not_lt_of_ge (Fin.le_last _))) A_zero A_succ
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_pred
+-/
 
+#print Matrix.det_eq_of_forall_col_eq_smul_add_pred /-
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ i, A i 0 = B i 0)
@@ -572,9 +684,11 @@ theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
   rw [← det_transpose A, ← det_transpose B]
   exact det_eq_of_forall_row_eq_smul_add_pred c A_zero fun i j => A_succ j i
 #align matrix.det_eq_of_forall_col_eq_smul_add_pred Matrix.det_eq_of_forall_col_eq_smul_add_pred
+-/
 
 end DetEq
 
+#print Matrix.det_blockDiagonal /-
 @[simp]
 theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Matrix n n R) :
     (blockDiagonal M).det = ∏ k, (M k).det :=
@@ -648,7 +762,9 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
     rw [← @Prod.mk.eta _ _ (σ (k, x)), block_diagonal_apply_ne]
     exact hkx
 #align matrix.det_block_diagonal Matrix.det_blockDiagonal
+-/
 
+#print Matrix.det_fromBlocks_zero₂₁ /-
 /-- The determinant of a 2×2 block matrix with the lower-left block equal to zero is the product of
 the determinants of the diagonal blocks. For the generalization to any number of blocks, see
 `matrix.det_of_upper_triangular`. -/
@@ -705,7 +821,9 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
       rw [hx, from_blocks_apply₂₁]; rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
+-/
 
+#print Matrix.det_fromBlocks_zero₁₂ /-
 /-- The determinant of a 2×2 block matrix with the upper-right block equal to zero is the product of
 the determinants of the diagonal blocks. For the generalization to any number of blocks, see
 `matrix.det_of_lower_triangular`. -/
@@ -715,6 +833,7 @@ theorem det_fromBlocks_zero₁₂ (A : Matrix m m R) (C : Matrix n m R) (D : Mat
   rw [← det_transpose, from_blocks_transpose, transpose_zero, det_from_blocks_zero₂₁, det_transpose,
     det_transpose]
 #align matrix.det_from_blocks_zero₁₂ Matrix.det_fromBlocks_zero₁₂
+-/
 
 #print Matrix.det_succ_column_zero /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along column 0. -/
@@ -803,16 +922,20 @@ theorem det_succ_column {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (j :
 #align matrix.det_succ_column Matrix.det_succ_column
 -/
 
+#print Matrix.det_fin_zero /-
 /-- Determinant of 0x0 matrix -/
 @[simp]
 theorem det_fin_zero {A : Matrix (Fin 0) (Fin 0) R} : det A = 1 :=
   det_isEmpty
 #align matrix.det_fin_zero Matrix.det_fin_zero
+-/
 
+#print Matrix.det_fin_one /-
 /-- Determinant of 1x1 matrix -/
 theorem det_fin_one (A : Matrix (Fin 1) (Fin 1) R) : det A = A 0 0 :=
   det_unique A
 #align matrix.det_fin_one Matrix.det_fin_one
+-/
 
 #print Matrix.det_fin_one_of /-
 theorem det_fin_one_of (a : R) : det !![a] = a :=
@@ -820,12 +943,14 @@ theorem det_fin_one_of (a : R) : det !![a] = a :=
 #align matrix.det_fin_one_of Matrix.det_fin_one_of
 -/
 
+#print Matrix.det_fin_two /-
 /-- Determinant of 2x2 matrix -/
 theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0 1 * A 1 0 :=
   by
   simp [Matrix.det_succ_row_zero, Fin.sum_univ_succ]
   ring
 #align matrix.det_fin_two Matrix.det_fin_two
+-/
 
 #print Matrix.det_fin_two_of /-
 @[simp]

86d1873c

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -143,7 +143,7 @@ theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (
 #align matrix.det_eq_elem_of_card_eq_one Matrix.det_eq_elem_of_card_eq_one
 
 theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
-    (∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x) = 0 :=
+    ∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x = 0 :=
   by
   obtain ⟨i, j, hpij, hij⟩ : ∃ i j, p i = p j ∧ i ≠ j :=
     by
@@ -154,7 +154,7 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     sum_involution (fun σ _ => σ * swap i j)
       (fun σ _ =>
         by
-        have : (∏ x, M (σ x) (p x)) = ∏ x, M ((σ * swap i j) x) (p x) :=
+        have : ∏ x, M (σ x) (p x) = ∏ x, M ((σ * swap i j) x) (p x) :=
           Fintype.prod_equiv (swap i j) _ _ (by simp [apply_swap_eq_self hpij])
         simp [this, sign_swap hij, prod_mul_distrib])
       (fun σ _ _ => (not_congr mul_swap_eq_iff).mpr hij) (fun _ _ => mem_univ _) fun σ _ =>
@@ -183,7 +183,7 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
       (sum_congr rfl fun σ _ =>
         Fintype.sum_equiv (Equiv.mulRight σ⁻¹) _ _ fun τ =>
           by
-          have : (∏ j, M (τ j) (σ j)) = ∏ j, M ((τ * σ⁻¹) j) j := by rw [← (σ⁻¹ : _ ≃ _).prod_comp];
+          have : ∏ j, M (τ j) (σ j) = ∏ j, M ((τ * σ⁻¹) j) j := by rw [← (σ⁻¹ : _ ≃ _).prod_comp];
             simp only [Equiv.Perm.coe_mul, apply_inv_self]
           have h : ε σ * ε (τ * σ⁻¹) = ε τ :=
             calc
@@ -740,7 +740,7 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   refine' Finset.sum_congr rfl fun σ _ => _
   rw [Equiv.Perm.decomposeFin.symm_sign, if_neg (Fin.succ_ne_zero i)]
   calc
-    ((-1 * σ.sign : ℤ) • ∏ i', A (equiv.perm.decompose_fin.symm (Fin.succ i, σ) i') i') =
+    (-1 * σ.sign : ℤ) • ∏ i', A (equiv.perm.decompose_fin.symm (Fin.succ i, σ) i') i' =
         (-1 * σ.sign : ℤ) •
           (A (Fin.succ i) 0 * ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) :=
       by

86d1873c

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -190,11 +190,9 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
               ε σ * ε (τ * σ⁻¹) = ε (τ * σ⁻¹ * σ) := by rw [mul_comm, sign_mul (τ * σ⁻¹)];
                 simp only [Int.cast_mul, Units.val_mul]
               _ = ε τ := by simp only [inv_mul_cancel_right]
-              
           simp_rw [Equiv.coe_mulRight, h]
           simp only [this])
     _ = det M * det N := by simp only [det_apply', Finset.mul_sum, mul_comm, mul_left_comm]
-    
 #align matrix.det_mul Matrix.det_mul
 
 #print Matrix.detMonoidHom /-
@@ -292,7 +290,6 @@ theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n
     det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
     _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
-    
 #align matrix.det_smul Matrix.det_smul
 
 @[simp]
@@ -319,7 +316,6 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     det (of fun i j => v j * A i j) = det (A ⬝ diagonal v) :=
       congr_arg det <| by ext; simp [mul_comm]
     _ = (∏ i, v i) * det A := by rw [det_mul, det_diagonal, mul_comm]
-    
 #align matrix.det_mul_row Matrix.det_mul_row
 
 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
@@ -444,7 +440,6 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     det A = det (B ⬝ C) := congr_arg _ hA
     _ = det B * det C := (det_mul _ _)
     _ = det B := by rw [hC, mul_one]
-    
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
 
 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
@@ -453,7 +448,6 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     det A = det (C ⬝ B) := congr_arg _ hA
     _ = det C * det B := (det_mul _ _)
     _ = det B := by rw [hC, one_mul]
-    
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul
 
 theorem det_updateRow_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
@@ -759,7 +753,6 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
       by
       simp only [mul_assoc, mul_comm, _root_.neg_mul, one_mul, zsmul_eq_mul, neg_inj, neg_smul,
         Fin.succAbove_cycleRange]
-    
 #align matrix.det_succ_column_zero Matrix.det_succ_column_zero
 -/
 
@@ -786,7 +779,6 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
     calc
       det A = ↑((-1 : ℤˣ) ^ (i : ℕ) * (-1 : ℤˣ) ^ (i : ℕ) : ℤˣ) * det A := by simp
       _ = (-1 : R) ^ (i : ℕ) * i.cycle_range⁻¹.sign * det A := by simp [-Int.units_mul_self]
-      
   rw [this, mul_assoc]
   congr
   rw [← det_permute, det_succ_row_zero]

86d1873c

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -148,7 +148,7 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
   obtain ⟨i, j, hpij, hij⟩ : ∃ i j, p i = p j ∧ i ≠ j :=
     by
     rw [← Finite.injective_iff_bijective, injective] at H 
-    push_neg  at H 
+    push_neg at H 
     exact H
   exact
     sum_involution (fun σ _ => σ * swap i j)
@@ -662,54 +662,54 @@ the determinants of the diagonal blocks. For the generalization to any number of
 theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Matrix n n R) :
     (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by
   classical
-    simp_rw [det_apply']
-    convert(sum_subset (subset_univ ((sum_congr_hom m n).range : Set (perm (Sum m n))).toFinset)
-          _).symm
-    rw [sum_mul_sum]
-    simp_rw [univ_product_univ]
-    rw [(sum_bij (fun (σ : perm m × perm n) _ => Equiv.sumCongr σ.fst σ.snd) _ _ _ _).symm]
-    · intro σ₁₂ h
-      simp only
-      erw [Set.mem_toFinset, MonoidHom.mem_range]
-      use σ₁₂
-      simp only [sum_congr_hom_apply]
-    · simp only [forall_prop_of_true, Prod.forall, mem_univ]
-      intro σ₁ σ₂
-      rw [Fintype.prod_sum_type]
-      simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, from_blocks_apply₁₁,
-        from_blocks_apply₂₂]
-      rw [mul_mul_mul_comm]
-      congr
-      rw [sign_sum_congr, Units.val_mul, Int.cast_mul]
-    · intro σ₁ σ₂ h₁ h₂
-      dsimp only
-      intro h
-      have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
-        exact congr_fun (congr_arg to_fun h) x
-      simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2 
-      ext
-      · exact h2.left x
-      · exact h2.right x
-    · intro σ hσ
-      erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ 
-      obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
-      use σ₁₂
-      rw [← hσ₁₂]
-      simp
-    · intro σ hσ hσn
-      have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) :=
-        by
-        by_contra
-        rw [Set.mem_toFinset] at hσn 
-        apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
-        rintro x ⟨a, ha⟩
-        rw [← ha]; exact h a
-      obtain ⟨a, ha⟩ := not_forall.mp h1
-      cases' hx : σ (Sum.inl a) with a2 b
-      · have hn := (not_exists.mp ha) a2
-        exact absurd hx.symm hn
-      · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
-        rw [hx, from_blocks_apply₂₁]; rfl
+  simp_rw [det_apply']
+  convert
+    (sum_subset (subset_univ ((sum_congr_hom m n).range : Set (perm (Sum m n))).toFinset) _).symm
+  rw [sum_mul_sum]
+  simp_rw [univ_product_univ]
+  rw [(sum_bij (fun (σ : perm m × perm n) _ => Equiv.sumCongr σ.fst σ.snd) _ _ _ _).symm]
+  · intro σ₁₂ h
+    simp only
+    erw [Set.mem_toFinset, MonoidHom.mem_range]
+    use σ₁₂
+    simp only [sum_congr_hom_apply]
+  · simp only [forall_prop_of_true, Prod.forall, mem_univ]
+    intro σ₁ σ₂
+    rw [Fintype.prod_sum_type]
+    simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, from_blocks_apply₁₁,
+      from_blocks_apply₂₂]
+    rw [mul_mul_mul_comm]
+    congr
+    rw [sign_sum_congr, Units.val_mul, Int.cast_mul]
+  · intro σ₁ σ₂ h₁ h₂
+    dsimp only
+    intro h
+    have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
+      exact congr_fun (congr_arg to_fun h) x
+    simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2 
+    ext
+    · exact h2.left x
+    · exact h2.right x
+  · intro σ hσ
+    erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ 
+    obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
+    use σ₁₂
+    rw [← hσ₁₂]
+    simp
+  · intro σ hσ hσn
+    have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) :=
+      by
+      by_contra
+      rw [Set.mem_toFinset] at hσn 
+      apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
+      rintro x ⟨a, ha⟩
+      rw [← ha]; exact h a
+    obtain ⟨a, ha⟩ := not_forall.mp h1
+    cases' hx : σ (Sum.inl a) with a2 b
+    · have hn := (not_exists.mp ha) a2
+      exact absurd hx.symm hn
+    · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
+      rw [hx, from_blocks_apply₂₁]; rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
 
 /-- The determinant of a 2×2 block matrix with the upper-right block equal to zero is the product of

86d1873c

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -147,8 +147,8 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
   by
   obtain ⟨i, j, hpij, hij⟩ : ∃ i j, p i = p j ∧ i ≠ j :=
     by
-    rw [← Finite.injective_iff_bijective, injective] at H
-    push_neg  at H
+    rw [← Finite.injective_iff_bijective, injective] at H 
+    push_neg  at H 
     exact H
   exact
     sum_involution (fun σ _ => σ * swap i j)
@@ -545,7 +545,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   have M_k : M k.cast_succ = M' k.cast_succ := (update_row_ne k_ne_succ).symm
   rw [hM, M_k, det_update_row_add_smul_self M' k_ne_succ.symm, ih (Function.update c k 0)]
   · intro i hi
-    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi
+    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi 
     rw [Function.update_apply]
     split_ifs with hik; · rfl
     exact hc _ (fin.succ_lt_succ_iff.mpr (lt_of_le_of_ne hi (Ne.symm hik)))
@@ -613,16 +613,16 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
       prod_congr_left_apply]
   · intro σ σ' _ _ eq
     ext (x hx k)
-    simp only at eq
+    simp only at eq 
     have :
       ∀ k x,
         prod_congr_left (fun k => σ k (Finset.mem_univ _)) (k, x) =
           prod_congr_left (fun k => σ' k (Finset.mem_univ _)) (k, x) :=
       fun k x => by rw [Eq]
-    simp only [prod_congr_left_apply, Prod.mk.inj_iff] at this
+    simp only [prod_congr_left_apply, Prod.mk.inj_iff] at this 
     exact (this k x).1
   · intro σ hσ
-    rw [mem_preserving_snd] at hσ
+    rw [mem_preserving_snd] at hσ 
     have hσ' : ∀ x, (σ⁻¹ x).snd = x.snd := by intro x;
       conv_rhs => rw [← perm.apply_inv_self σ x, hσ]
     have mk_apply_eq : ∀ k x, ((σ (x, k)).fst, k) = σ (x, k) :=
@@ -648,7 +648,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
       · simp only [coe_fn_mk, prod_congr_left_apply]
       · simp only [prod_congr_left_apply, hσ]
   · intro σ _ hσ
-    rw [mem_preserving_snd] at hσ
+    rw [mem_preserving_snd] at hσ 
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
     rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), MulZeroClass.mul_zero]
     rw [← @Prod.mk.eta _ _ (σ (k, x)), block_diagonal_apply_ne]
@@ -686,12 +686,12 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       intro h
       have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
         exact congr_fun (congr_arg to_fun h) x
-      simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2
+      simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2 
       ext
       · exact h2.left x
       · exact h2.right x
     · intro σ hσ
-      erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ
+      erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ 
       obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
       use σ₁₂
       rw [← hσ₁₂]
@@ -700,7 +700,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) :=
         by
         by_contra
-        rw [Set.mem_toFinset] at hσn
+        rw [Set.mem_toFinset] at hσn 
         apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
         rintro x ⟨a, ha⟩
         rw [← ha]; exact h a

86d1873c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -53,7 +53,7 @@ open Equiv Equiv.Perm Finset Function
 
 namespace Matrix
 
-open Matrix BigOperators
+open scoped Matrix BigOperators
 
 variable {m n : Type _} [DecidableEq n] [Fintype n] [DecidableEq m] [Fintype m]

86d1873c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -76,33 +76,15 @@ abbrev det (M : Matrix n n R) : R :=
 #align matrix.det Matrix.det
 -/
 
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-Case conversion may be inaccurate. Consider using '#align matrix.det_apply Matrix.det_applyₓ'. -/
 theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, σ.sign • ∏ i, M (σ i) i :=
   MultilinearMap.alternatization_apply _ M
 #align matrix.det_apply Matrix.det_apply
 
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 -- This is what the old definition was. We use it to avoid having to change the old proofs below
 theorem det_apply' (M : Matrix n n R) : M.det = ∑ σ : Perm n, ε σ * ∏ i, M (σ i) i := by
   simp [det_apply, Units.smul_def]
 #align matrix.det_apply' Matrix.det_apply'
 
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 @[simp]
 theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   by
@@ -118,64 +100,28 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
 
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 @[simp]
 theorem det_zero (h : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
 #align matrix.det_zero Matrix.det_zero
 
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 @[simp]
 theorem det_one : det (1 : Matrix n n R) = 1 := by rw [← diagonal_one] <;> simp [-diagonal_one]
 #align matrix.det_one Matrix.det_one
 
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 theorem det_isEmpty [IsEmpty n] {A : Matrix n n R} : det A = 1 := by simp [det_apply]
 #align matrix.det_is_empty Matrix.det_isEmpty
 
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 @[simp]
 theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.const _ 1 := by ext;
   exact det_is_empty
 #align matrix.coe_det_is_empty Matrix.coe_det_isEmpty
 
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 theorem det_eq_one_of_card_eq_zero {A : Matrix n n R} (h : Fintype.card n = 0) : det A = 1 :=
   haveI : IsEmpty n := fintype.card_eq_zero_iff.mp h
   det_is_empty
 #align matrix.det_eq_one_of_card_eq_zero Matrix.det_eq_one_of_card_eq_zero
 
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 /-- If `n` has only one element, the determinant of an `n` by `n` matrix is just that element.
 Although `unique` implies `decidable_eq` and `fintype`, the instances might
 not be syntactically equal. Thus, we need to fill in the args explicitly. -/
@@ -184,33 +130,18 @@ theorem det_unique {n : Type _} [Unique n] [DecidableEq n] [Fintype n] (A : Matr
     det A = A default default := by simp [det_apply, univ_unique]
 #align matrix.det_unique Matrix.det_unique
 
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 theorem det_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) : det A = A k k :=
   by
   convert det_unique _
   exact uniqueOfSubsingleton k
 #align matrix.det_eq_elem_of_subsingleton Matrix.det_eq_elem_of_subsingleton
 
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 theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (k : n) :
     det A = A k k :=
   haveI : Subsingleton n := fintype.card_le_one_iff_subsingleton.mp h.le
   det_eq_elem_of_subsingleton _ _
 #align matrix.det_eq_elem_of_card_eq_one Matrix.det_eq_elem_of_card_eq_one
 
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-<too large>
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 theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     (∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x) = 0 :=
   by
@@ -230,12 +161,6 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
       mul_swap_involutive i j σ
 #align matrix.det_mul_aux Matrix.det_mul_aux
 
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 @[simp]
 theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
   calc
@@ -281,78 +206,36 @@ def detMonoidHom : Matrix n n R →* R where
 #align matrix.det_monoid_hom Matrix.detMonoidHom
 -/
 
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 @[simp]
 theorem coe_detMonoidHom : (detMonoidHom : Matrix n n R → R) = det :=
   rfl
 #align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHom
 
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 /-- On square matrices, `mul_comm` applies under `det`. -/
 theorem det_mul_comm (M N : Matrix m m R) : det (M ⬝ N) = det (N ⬝ M) := by
   rw [det_mul, det_mul, mul_comm]
 #align matrix.det_mul_comm Matrix.det_mul_comm
 
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 /-- On square matrices, `mul_left_comm` applies under `det`. -/
 theorem det_mul_left_comm (M N P : Matrix m m R) : det (M ⬝ (N ⬝ P)) = det (N ⬝ (M ⬝ P)) := by
   rw [← Matrix.mul_assoc, ← Matrix.mul_assoc, det_mul, det_mul_comm M N, ← det_mul]
 #align matrix.det_mul_left_comm Matrix.det_mul_left_comm
 
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 /-- On square matrices, `mul_right_comm` applies under `det`. -/
 theorem det_mul_right_comm (M N P : Matrix m m R) : det (M ⬝ N ⬝ P) = det (M ⬝ P ⬝ N) := by
   rw [Matrix.mul_assoc, Matrix.mul_assoc, det_mul, det_mul_comm N P, ← det_mul]
 #align matrix.det_mul_right_comm Matrix.det_mul_right_comm
 
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 theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M ⬝ N ⬝ ↑M⁻¹ : Matrix m m R) = det N := by
   rw [det_mul_right_comm, ← mul_eq_mul, ← mul_eq_mul, Units.mul_inv, one_mul]
 #align matrix.det_units_conj Matrix.det_units_conj
 
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 theorem det_units_conj' (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M⁻¹ ⬝ N ⬝ ↑M : Matrix m m R) = det N :=
   det_units_conj M⁻¹ N
 #align matrix.det_units_conj' Matrix.det_units_conj'
 
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 /-- Transposing a matrix preserves the determinant. -/
 @[simp]
 theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
@@ -367,24 +250,12 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
   simp
 #align matrix.det_transpose Matrix.det_transpose
 
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 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = σ.sign * M.det :=
   ((detRowAlternating : AlternatingMap R (n → R) R n).map_perm M σ).trans (by simp [Units.smul_def])
 #align matrix.det_permute Matrix.det_permute
 
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 /-- Permuting rows and columns with the same equivalence has no effect. -/
 @[simp]
 theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.submatrix e e) = det A :=
@@ -399,12 +270,6 @@ theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.subma
   rw [Equiv.permCongr_apply, Equiv.symm_apply_apply, submatrix_apply]
 #align matrix.det_submatrix_equiv_self Matrix.det_submatrix_equiv_self
 
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 /-- Reindexing both indices along the same equivalence preserves the determinant.
 
 For the `simp` version of this lemma, see `det_submatrix_equiv_self`; this one is unsuitable because
@@ -414,12 +279,6 @@ theorem det_reindex_self (e : m ≃ n) (A : Matrix m m R) : det (reindex e e A)
   det_submatrix_equiv_self e.symm A
 #align matrix.det_reindex_self Matrix.det_reindex_self
 
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 /-- The determinant of a permutation matrix equals its sign. -/
 @[simp]
 theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matrix n n R) = σ.sign :=
@@ -428,12 +287,6 @@ theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matri
     det_permute, det_one, mul_one]
 #align matrix.det_permutation Matrix.det_permutation
 
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 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
     det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
@@ -442,46 +295,22 @@ theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n
     
 #align matrix.det_smul Matrix.det_smul
 
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 @[simp]
 theorem det_smul_of_tower {α} [Monoid α] [DistribMulAction α R] [IsScalarTower α R R]
     [SMulCommClass α R R] (c : α) (A : Matrix n n R) : det (c • A) = c ^ Fintype.card n • det A :=
   by rw [← smul_one_smul R c A, det_smul, smul_pow, one_pow, smul_mul_assoc, one_mul]
 #align matrix.det_smul_of_tower Matrix.det_smul_of_tower
 
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 theorem det_neg (A : Matrix n n R) : det (-A) = (-1) ^ Fintype.card n * det A := by
   rw [← det_smul, neg_one_smul]
 #align matrix.det_neg Matrix.det_neg
 
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 /-- A variant of `matrix.det_neg` with scalar multiplication by `units ℤ` instead of multiplication
 by `R`. -/
 theorem det_neg_eq_smul (A : Matrix n n R) : det (-A) = (-1 : Units ℤ) ^ Fintype.card n • det A :=
   by rw [← det_smul_of_tower, Units.neg_smul, one_smul]
 #align matrix.det_neg_eq_smul Matrix.det_neg_eq_smul
 
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 /-- Multiplying each row by a fixed `v i` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_row (v : n → R) (A : Matrix n n R) :
@@ -493,12 +322,6 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     
 #align matrix.det_mul_row Matrix.det_mul_row
 
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 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_column (v : n → R) (A : Matrix n n R) :
@@ -506,12 +329,6 @@ theorem det_mul_column (v : n → R) (A : Matrix n n R) :
   MultilinearMap.map_smul_univ _ v A
 #align matrix.det_mul_column Matrix.det_mul_column
 
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 @[simp]
 theorem det_pow (M : Matrix m m R) (n : ℕ) : det (M ^ n) = det M ^ n :=
   (detMonoidHom : Matrix m m R →* R).map_pow M n
@@ -521,31 +338,19 @@ section HomMap
 
 variable {S : Type w} [CommRing S]
 
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 theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
 #align ring_hom.map_det RingHom.map_det
 
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 theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align ring_equiv.map_det RingEquiv.map_det
 
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 theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S →ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align alg_hom.map_det AlgHom.map_det
 
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 theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S ≃ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toAlgHom.map_det _
@@ -553,12 +358,6 @@ theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (
 
 end HomMap
 
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 @[simp]
 theorem det_conjTranspose [StarRing R] (M : Matrix m m R) : det Mᴴ = star (det M) :=
   ((starRingEnd R).map_det _).symm.trans <| congr_arg star M.det_transpose
@@ -573,45 +372,21 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 -/
 
 
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 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
 
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 theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) : det A = 0 :=
   by rw [← det_transpose]; exact det_eq_zero_of_row_eq_zero j h
 #align matrix.det_eq_zero_of_column_eq_zero Matrix.det_eq_zero_of_column_eq_zero
 
 variable {M : Matrix n n R} {i j : n}
 
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 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_eq_zero_of_eq M hij i_ne_j
 #align matrix.det_zero_of_row_eq Matrix.det_zero_of_row_eq
 
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 /-- If a matrix has a repeated column, the determinant will be zero. -/
 theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) : M.det = 0 := by
   rw [← det_transpose, det_zero_of_row_eq i_ne_j]; exact funext hij
@@ -619,23 +394,11 @@ theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) :
 
 end DetZero
 
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 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_add M j u v
 #align matrix.det_update_row_add Matrix.det_updateRow_add
 
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 theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateColumn M j <| u + v) = det (updateColumn M j u) + det (updateColumn M j v) :=
   by
@@ -643,23 +406,11 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_add Matrix.det_updateColumn_add
 
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 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_smul M j s u
 #align matrix.det_update_row_smul Matrix.det_updateRow_smul
 
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 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=
   by
@@ -667,23 +418,11 @@ theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_smul Matrix.det_updateColumn_smul
 
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 theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateRow M j u) :=
   MultilinearMap.map_update_smul _ M j s u
 #align matrix.det_update_row_smul' Matrix.det_updateRow_smul'
 
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 theorem det_updateColumn_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateColumn M j u) :=
   by
@@ -699,12 +438,6 @@ Lemmas showing the determinant is invariant under a variety of operations.
 -/
 
 
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 theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = B ⬝ C) : det A = det B :=
   calc
@@ -714,12 +447,6 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
 
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 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = C ⬝ B) : det A = det B :=
   calc
@@ -729,24 +456,12 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul
 
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 theorem det_updateRow_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
     det (updateRow A i (A i + A j)) = det A := by
   simp [det_update_row_add,
     det_zero_of_row_eq hij (update_row_self.trans (update_row_ne hij.symm).symm)]
 #align matrix.det_update_row_add_self Matrix.det_updateRow_add_self
 
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 theorem det_updateColumn_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
     det (updateColumn A i fun k => A k i + A k j) = det A :=
   by
@@ -754,24 +469,12 @@ theorem det_updateColumn_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
   exact det_update_row_add_self Aᵀ hij
 #align matrix.det_update_column_add_self Matrix.det_updateColumn_add_self
 
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 theorem det_updateRow_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateRow A i (A i + c • A j)) = det A := by
   simp [det_update_row_add, det_update_row_smul,
     det_zero_of_row_eq hij (update_row_self.trans (update_row_ne hij.symm).symm)]
 #align matrix.det_update_row_add_smul_self Matrix.det_updateRow_add_smul_self
 
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 theorem det_updateColumn_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateColumn A i fun k => A k i + c • A k j) = det A :=
   by
@@ -779,12 +482,6 @@ theorem det_updateColumn_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠
   exact det_update_row_add_smul_self Aᵀ hij c
 #align matrix.det_update_column_add_smul_self Matrix.det_updateColumn_add_smul_self
 
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 theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Finset n} :
     ∀ (c : n → R) (hs : ∀ i, i ∉ s → c i = 0) (k : n) (hk : k ∉ s)
       (A_eq : ∀ i j, A i j = B i j + c i * B k j), det A = det B :=
@@ -816,12 +513,6 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       rw [A_eq, update_row_ne fun h : k = i => hk <| h ▸ Finset.mem_insert_self k s]
 #align matrix.det_eq_of_forall_row_eq_smul_add_const_aux Matrix.det_eq_of_forall_row_eq_smul_add_const_aux
 
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 /-- If you add multiples of row `B k` to other rows, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R) (k : n)
     (hk : c k = 0) (A_eq : ∀ i j, A i j = B i j + c i * B k j) : det A = det B :=
@@ -833,9 +524,6 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
     k (Finset.not_mem_erase k Finset.univ) A_eq
 #align matrix.det_eq_of_forall_row_eq_smul_add_const Matrix.det_eq_of_forall_row_eq_smul_add_const
 
-/- warning: matrix.det_eq_of_forall_row_eq_smul_add_pred_aux -> Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_auxₓ'. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (hc : ∀ i : Fin n, k < i.succ → c i = 0)
       {M N : Matrix (Fin n.succ) (Fin n.succ) R} (h0 : ∀ j, M 0 j = N 0 j)
@@ -874,9 +562,6 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 
-/- warning: matrix.det_eq_of_forall_row_eq_smul_add_pred -> Matrix.det_eq_of_forall_row_eq_smul_add_pred is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ j, A 0 j = B 0 j)
@@ -885,9 +570,6 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
     (fun i hi => absurd hi (not_lt_of_ge (Fin.le_last _))) A_zero A_succ
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_pred
 
-/- warning: matrix.det_eq_of_forall_col_eq_smul_add_pred -> Matrix.det_eq_of_forall_col_eq_smul_add_pred is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_col_eq_smul_add_pred Matrix.det_eq_of_forall_col_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ i, A i 0 = B i 0)
@@ -899,12 +581,6 @@ theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 
 end DetEq
 
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 @[simp]
 theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Matrix n n R) :
     (blockDiagonal M).det = ∏ k, (M k).det :=
@@ -979,12 +655,6 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
     exact hkx
 #align matrix.det_block_diagonal Matrix.det_blockDiagonal
 
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 /-- The determinant of a 2×2 block matrix with the lower-left block equal to zero is the product of
 the determinants of the diagonal blocks. For the generalization to any number of blocks, see
 `matrix.det_of_upper_triangular`. -/
@@ -1042,12 +712,6 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
         rw [hx, from_blocks_apply₂₁]; rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
 
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 /-- The determinant of a 2×2 block matrix with the upper-right block equal to zero is the product of
 the determinants of the diagonal blocks. For the generalization to any number of blocks, see
 `matrix.det_of_lower_triangular`. -/
@@ -1147,24 +811,12 @@ theorem det_succ_column {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (j :
 #align matrix.det_succ_column Matrix.det_succ_column
 -/
 
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 /-- Determinant of 0x0 matrix -/
 @[simp]
 theorem det_fin_zero {A : Matrix (Fin 0) (Fin 0) R} : det A = 1 :=
   det_isEmpty
 #align matrix.det_fin_zero Matrix.det_fin_zero
 
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 /-- Determinant of 1x1 matrix -/
 theorem det_fin_one (A : Matrix (Fin 1) (Fin 1) R) : det A = A 0 0 :=
   det_unique A
@@ -1176,12 +828,6 @@ theorem det_fin_one_of (a : R) : det !![a] = a :=
 #align matrix.det_fin_one_of Matrix.det_fin_one_of
 -/
 
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Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) R), Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (b : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) R _inst_5 A) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_5))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))
-Case conversion may be inaccurate. Consider using '#align matrix.det_fin_two Matrix.det_fin_twoₓ'. -/
 /-- Determinant of 2x2 matrix -/
 theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0 1 * A 1 0 :=
   by

86d1873c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -112,8 +112,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
     cases' not_forall.1 (mt Equiv.ext h2) with x h3
     convert MulZeroClass.mul_zero _
     apply Finset.prod_eq_zero
-    · change x ∈ _
-      simp
+    · change x ∈ _; simp
     exact if_neg h3
   · simp
   · simp
@@ -156,9 +155,7 @@ but is expected to have type
   forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : IsEmpty.{succ u1} n], Eq.{max (succ u2) (succ u1)} ((Matrix.{u1, u1, u2} n n R) -> R) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5) (Function.const.{succ u2, max (succ u2) (succ u1)} R (Matrix.{u1, u1, u2} n n R) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align matrix.coe_det_is_empty Matrix.coe_det_isEmptyₓ'. -/
 @[simp]
-theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.const _ 1 :=
-  by
-  ext
+theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.const _ 1 := by ext;
   exact det_is_empty
 #align matrix.coe_det_is_empty Matrix.coe_det_isEmpty
 
@@ -261,15 +258,11 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
       (sum_congr rfl fun σ _ =>
         Fintype.sum_equiv (Equiv.mulRight σ⁻¹) _ _ fun τ =>
           by
-          have : (∏ j, M (τ j) (σ j)) = ∏ j, M ((τ * σ⁻¹) j) j :=
-            by
-            rw [← (σ⁻¹ : _ ≃ _).prod_comp]
+          have : (∏ j, M (τ j) (σ j)) = ∏ j, M ((τ * σ⁻¹) j) j := by rw [← (σ⁻¹ : _ ≃ _).prod_comp];
             simp only [Equiv.Perm.coe_mul, apply_inv_self]
           have h : ε σ * ε (τ * σ⁻¹) = ε τ :=
             calc
-              ε σ * ε (τ * σ⁻¹) = ε (τ * σ⁻¹ * σ) :=
-                by
-                rw [mul_comm, sign_mul (τ * σ⁻¹)]
+              ε σ * ε (τ * σ⁻¹) = ε (τ * σ⁻¹ * σ) := by rw [mul_comm, sign_mul (τ * σ⁻¹)];
                 simp only [Int.cast_mul, Units.val_mul]
               _ = ε τ := by simp only [inv_mul_cancel_right]
               
@@ -495,9 +488,7 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     det (of fun i j => v j * A i j) = (∏ i, v i) * det A :=
   calc
     det (of fun i j => v j * A i j) = det (A ⬝ diagonal v) :=
-      congr_arg det <| by
-        ext
-        simp [mul_comm]
+      congr_arg det <| by ext; simp [mul_comm]
     _ = (∏ i, v i) * det A := by rw [det_mul, det_diagonal, mul_comm]
     
 #align matrix.det_mul_row Matrix.det_mul_row
@@ -599,9 +590,7 @@ but is expected to have type
   forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R} (j : n), (forall (i : n), Eq.{succ u2} R (A i j) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_zero_of_column_eq_zero Matrix.det_eq_zero_of_column_eq_zeroₓ'. -/
 theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) : det A = 0 :=
-  by
-  rw [← det_transpose]
-  exact det_eq_zero_of_row_eq_zero j h
+  by rw [← det_transpose]; exact det_eq_zero_of_row_eq_zero j h
 #align matrix.det_eq_zero_of_column_eq_zero Matrix.det_eq_zero_of_column_eq_zero
 
 variable {M : Matrix n n R} {i j : n}
@@ -624,10 +613,8 @@ but is expected to have type
   forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {M : Matrix.{u1, u1, u2} n n R} {i : n} {j : n}, (Ne.{succ u1} n i j) -> (forall (k : n), Eq.{succ u2} R (M k i) (M k j)) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_zero_of_column_eq Matrix.det_zero_of_column_eqₓ'. -/
 /-- If a matrix has a repeated column, the determinant will be zero. -/
-theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) : M.det = 0 :=
-  by
-  rw [← det_transpose, det_zero_of_row_eq i_ne_j]
-  exact funext hij
+theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) : M.det = 0 := by
+  rw [← det_transpose, det_zero_of_row_eq i_ne_j]; exact funext hij
 #align matrix.det_zero_of_column_eq Matrix.det_zero_of_column_eq
 
 end DetZero
@@ -819,8 +806,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
     · exact mt (fun h => show k ∈ insert i s from h ▸ Finset.mem_insert_self _ _) hk
     · intro i' hi'
       rw [Function.update_apply]
-      split_ifs with hi'i
-      · rfl
+      split_ifs with hi'i; · rfl
       · exact hs i' fun h => hi' ((finset.mem_insert.mp h).resolve_left hi'i)
     · exact fun h => hk (Finset.mem_insert_of_mem h)
     · intro i' j'
@@ -873,8 +859,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · intro i hi
     rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi
     rw [Function.update_apply]
-    split_ifs with hik
-    · rfl
+    split_ifs with hik; · rfl
     exact hc _ (fin.succ_lt_succ_iff.mpr (lt_of_le_of_ne hi (Ne.symm hik)))
   · rwa [hM', update_row_ne (Fin.succ_ne_zero _).symm]
   intro i j
@@ -962,8 +947,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
     exact (this k x).1
   · intro σ hσ
     rw [mem_preserving_snd] at hσ
-    have hσ' : ∀ x, (σ⁻¹ x).snd = x.snd := by
-      intro x
+    have hσ' : ∀ x, (σ⁻¹ x).snd = x.snd := by intro x;
       conv_rhs => rw [← perm.apply_inv_self σ x, hσ]
     have mk_apply_eq : ∀ k x, ((σ (x, k)).fst, k) = σ (x, k) :=
       by
@@ -1030,9 +1014,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     · intro σ₁ σ₂ h₁ h₂
       dsimp only
       intro h
-      have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x :=
-        by
-        intro x
+      have h2 : ∀ x, perm.sum_congr σ₁.fst σ₁.snd x = perm.sum_congr σ₂.fst σ₂.snd x := by intro x;
         exact congr_fun (congr_arg to_fun h) x
       simp only [Sum.map_inr, Sum.map_inl, perm.sum_congr_apply, Sum.forall] at h2
       ext
@@ -1051,15 +1033,13 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
         rw [Set.mem_toFinset] at hσn
         apply absurd (mem_sum_congr_hom_range_of_perm_maps_to_inl _) hσn
         rintro x ⟨a, ha⟩
-        rw [← ha]
-        exact h a
+        rw [← ha]; exact h a
       obtain ⟨a, ha⟩ := not_forall.mp h1
       cases' hx : σ (Sum.inl a) with a2 b
       · have hn := (not_exists.mp ha) a2
         exact absurd hx.symm hn
       · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
-        rw [hx, from_blocks_apply₂₁]
-        rfl
+        rw [hx, from_blocks_apply₂₁]; rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
 
 /- warning: matrix.det_from_blocks_zero₁₂ -> Matrix.det_fromBlocks_zero₁₂ is a dubious translation:

86d1873c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -212,10 +212,7 @@ theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (
 #align matrix.det_eq_elem_of_card_eq_one Matrix.det_eq_elem_of_card_eq_one
 
 /- warning: matrix.det_mul_aux -> Matrix.det_mul_aux is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_mul_aux Matrix.det_mul_auxₓ'. -/
 theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     (∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x) = 0 :=
@@ -534,30 +531,21 @@ section HomMap
 variable {S : Type w} [CommRing S]
 
 /- warning: ring_hom.map_det -> RingHom.map_det is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align ring_hom.map_det RingHom.map_detₓ'. -/
 theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
 #align ring_hom.map_det RingHom.map_det
 
 /- warning: ring_equiv.map_det -> RingEquiv.map_det is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ring_equiv.map_det RingEquiv.map_detₓ'. -/
 theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align ring_equiv.map_det RingEquiv.map_det
 
 /- warning: alg_hom.map_det -> AlgHom.map_det is a dubious translation:
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a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.map_det AlgHom.map_detₓ'. -/
 theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S →ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
@@ -565,10 +553,7 @@ theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f
 #align alg_hom.map_det AlgHom.map_det
 
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(CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9)))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T 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n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)))))) (SMulZeroClass.toSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toZero.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toAddZeroClass.{max u4 u1} (Matrix.{u1, u1, u4} n n T) 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(Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgEquivClass.toAlgHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))))) (AlgEquiv.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_equiv.map_det AlgEquiv.map_detₓ'. -/
 theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S ≃ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
@@ -863,10 +848,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
 #align matrix.det_eq_of_forall_row_eq_smul_add_const Matrix.det_eq_of_forall_row_eq_smul_add_const
 
 /- warning: matrix.det_eq_of_forall_row_eq_smul_add_pred_aux -> Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_auxₓ'. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (hc : ∀ i : Fin n, k < i.succ → c i = 0)
@@ -908,10 +890,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
@@ -922,10 +901,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_pred
 
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Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin n) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc n) j))))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 A) (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 B))
+<too large>
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_col_eq_smul_add_pred Matrix.det_eq_of_forall_col_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}

86d1873c

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -557,7 +557,7 @@ theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.
 lean 3 declaration is
   forall {n : Type.{u4}} [_inst_1 : DecidableEq.{succ u4} n] [_inst_2 : Fintype.{u4} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] {T : Type.{u3}} [_inst_8 : CommRing.{u3} T] [_inst_9 : Algebra.{u1, u3} R T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8))] (f : AlgHom.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u4, u4, u2} n n S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) => S -> T) ([anonymous].{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) f (Matrix.det.{u2, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u3, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (coeFn.{max (succ (max u4 u2)) (succ (max u4 u3)), max (succ (max u4 u2)) (succ (max u4 u3))} (AlgHom.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (fun (_x : AlgHom.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) => (Matrix.{u4, u4, u2} n n S) -> (Matrix.{u4, u4, u3} n n T)) ([anonymous].{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (AlgHom.mapMatrix.{u2, u3, u4, u1} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9 f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))] (f : AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T 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a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.algHomClass.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (AlgHom.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))] (f : AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) 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a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.algHomClass.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (AlgHom.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
 Case conversion may be inaccurate. Consider using '#align alg_hom.map_det AlgHom.map_detₓ'. -/
 theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S →ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
@@ -568,7 +568,7 @@ theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f
 lean 3 declaration is
   forall {n : Type.{u4}} [_inst_1 : DecidableEq.{succ u4} n] [_inst_2 : Fintype.{u4} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] {T : Type.{u3}} [_inst_8 : CommRing.{u3} T] [_inst_9 : Algebra.{u1, u3} R T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8))] (f : AlgEquiv.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u4, u4, u2} n n S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgEquiv.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (fun (_x : AlgEquiv.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) => S -> T) (AlgEquiv.hasCoeToFun.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) f (Matrix.det.{u2, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u3, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (coeFn.{max (succ (max u4 u2)) (succ (max u4 u3)), max (succ (max u4 u2)) (succ (max u4 u3))} (AlgEquiv.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (fun (_x : AlgEquiv.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) => (Matrix.{u4, u4, u2} n n S) -> (Matrix.{u4, u4, u3} n n T)) (AlgEquiv.hasCoeToFun.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (AlgEquiv.mapMatrix.{u2, u3, u4, u1} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9 f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))] (f : AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9)))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T 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n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)))))) (SMulZeroClass.toSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toZero.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toAddZeroClass.{max u4 u1} (Matrix.{u1, u1, u4} n n T) 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(Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgEquivClass.toAlgHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))))) (AlgEquiv.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))] (f : AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9)))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (Matrix.{u1, u1, u3} n n S) (fun (_x : Matrix.{u1, u1, u3} n n S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u1, u1, u3} n n S) => Matrix.{u1, u1, u4} n n T) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (SMulZeroClass.toSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)))))) (SMulZeroClass.toSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toZero.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toAddZeroClass.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgEquivClass.toAlgHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))))) (AlgEquiv.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
 Case conversion may be inaccurate. Consider using '#align alg_equiv.map_det AlgEquiv.map_detₓ'. -/
 theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S ≃ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=

86d1873c

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -80,7 +80,7 @@ abbrev det (M : Matrix n n R) : R :=
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (Finset.sum.{u1, u2} R (Equiv.Perm.{succ u2} n) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Finset.univ.{u2} (Equiv.Perm.{succ u2} n) (Equiv.fintype.{u2, u2} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u2} n) => SMul.smul.{0, u1} (Units.{0} Int Int.monoid) R (Units.hasSmul.{0, u1} Int R Int.monoid (SubNegMonoid.SMulInt.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} n) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ) (Finset.prod.{u1, u2} R n (CommRing.toCommMonoid.{u1} R _inst_5) (Finset.univ.{u2} n _inst_2) (fun (i : n) => M (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} n) (fun (_x : Equiv.{succ u2, succ u2} n n) => n -> n) (Equiv.hasCoeToFun.{succ u2, succ u2} n n) σ i) i))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (Finset.sum.{u2, u1} R (Equiv.Perm.{succ u1} n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.univ.{u1} (Equiv.Perm.{succ u1} n) (equivFintype.{u1, u1} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u1} n) => HSMul.hSMul.{0, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) σ) R R (instHSMul.{0, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) σ) R (Units.instSMulUnits.{0, u2} Int R Int.instMonoidInt (SubNegMonoid.SMulInt.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (_x : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ i) i))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (Finset.sum.{u2, u1} R (Equiv.Perm.{succ u1} n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.univ.{u1} (Equiv.Perm.{succ u1} n) (equivFintype.{u1, u1} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u1} n) => HSMul.hSMul.{0, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) σ) R R (instHSMul.{0, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) σ) R (Units.instSMulUnits.{0, u2} Int R Int.instMonoidInt (SubNegMonoid.SMulInt.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (_x : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ i) i))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_apply Matrix.det_applyₓ'. -/
 theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, σ.sign • ∏ i, M (σ i) i :=
   MultilinearMap.alternatization_apply _ M
@@ -90,7 +90,7 @@ theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, σ.sign • ∏
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (Finset.sum.{u1, u2} R (Equiv.Perm.{succ u2} n) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Finset.univ.{u2} (Equiv.Perm.{succ u2} n) (Equiv.fintype.{u2, u2} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u2} n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Units.{0} Int Int.monoid) Int (HasLiftT.mk.{1, 1} (Units.{0} Int Int.monoid) Int (CoeTCₓ.coe.{1, 1} (Units.{0} Int Int.monoid) Int (coeBase.{1, 1} (Units.{0} Int Int.monoid) Int (Units.hasCoe.{0} Int Int.monoid)))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} n) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Finset.prod.{u1, u2} R n (CommRing.toCommMonoid.{u1} R _inst_5) (Finset.univ.{u2} n _inst_2) (fun (i : n) => M (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} n) (fun (_x : Equiv.{succ u2, succ u2} n n) => n -> n) (Equiv.hasCoeToFun.{succ u2, succ u2} n n) σ i) i))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (Finset.sum.{u2, u1} R (Equiv.Perm.{succ u1} n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.univ.{u1} (Equiv.Perm.{succ u1} n) (equivFintype.{u1, u1} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u1} n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (_x : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ i) i))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M) (Finset.sum.{u2, u1} R (Equiv.Perm.{succ u1} n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.univ.{u1} (Equiv.Perm.{succ u1} n) (equivFintype.{u1, u1} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u1} n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (_x : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ i) i))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_apply' Matrix.det_apply'ₓ'. -/
 -- This is what the old definition was. We use it to avoid having to change the old proofs below
 theorem det_apply' (M : Matrix n n R) : M.det = ∑ σ : Perm n, ε σ * ∏ i, M (σ i) i := by
@@ -215,7 +215,7 @@ theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {M : Matrix.{u2, u2, u1} n n R} {N : Matrix.{u2, u2, u1} n n R} {p : n -> n}, (Not (Function.Bijective.{succ u2, succ u2} n n p)) -> (Eq.{succ u1} R (Finset.sum.{u1, u2} R (Equiv.Perm.{succ u2} n) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Finset.univ.{u2} (Equiv.Perm.{succ u2} n) (Equiv.fintype.{u2, u2} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u2} n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int R (HasLiftT.mk.{1, succ u1} Int R (CoeTCₓ.coe.{1, succ u1} Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Units.{0} Int Int.monoid) Int (HasLiftT.mk.{1, 1} (Units.{0} Int Int.monoid) Int (CoeTCₓ.coe.{1, 1} (Units.{0} Int Int.monoid) Int (coeBase.{1, 1} (Units.{0} Int Int.monoid) Int (Units.hasCoe.{0} Int Int.monoid)))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} n) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Finset.prod.{u1, u2} R n (CommRing.toCommMonoid.{u1} R _inst_5) (Finset.univ.{u2} n _inst_2) (fun (x : n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (M (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} n) (fun (_x : Equiv.{succ u2, succ u2} n n) => n -> n) (Equiv.hasCoeToFun.{succ u2, succ u2} n n) σ x) (p x)) (N (p x) x))))) (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_5))))))))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {M : Matrix.{u1, u1, u2} n n R} {N : Matrix.{u1, u1, u2} n n R} {p : n -> n}, (Not (Function.Bijective.{succ u1, succ u1} n n p)) -> (Eq.{succ u2} R (Finset.sum.{u2, u1} R (Equiv.Perm.{succ u1} n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.univ.{u1} (Equiv.Perm.{succ u1} n) (equivFintype.{u1, u1} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u1} n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (_x : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (x : n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ x) (p x)) (N (p x) x))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {M : Matrix.{u1, u1, u2} n n R} {N : Matrix.{u1, u1, u2} n n R} {p : n -> n}, (Not (Function.Bijective.{succ u1, succ u1} n n p)) -> (Eq.{succ u2} R (Finset.sum.{u2, u1} R (Equiv.Perm.{succ u1} n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.univ.{u1} (Equiv.Perm.{succ u1} n) (equivFintype.{u1, u1} n n (fun (a : n) (b : n) => _inst_1 a b) (fun (a : n) (b : n) => _inst_1 a b) _inst_2 _inst_2)) (fun (σ : Equiv.Perm.{succ u1} n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (_x : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) _x) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (x : n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ x) (p x)) (N (p x) x))))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_mul_aux Matrix.det_mul_auxₓ'. -/
 theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     (∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x) = 0 :=
@@ -295,7 +295,7 @@ def detMonoidHom : Matrix n n R →* R where
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R], Eq.{max (succ (max u2 u1)) (succ u1)} ((fun (_x : MonoidHom.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) => (Matrix.{u2, u2, u1} n n R) -> R) (Matrix.detMonoidHom.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ (max u2 u1)) (succ u1)} (MonoidHom.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (fun (_x : MonoidHom.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) => (Matrix.{u2, u2, u1} n n R) -> R) (MonoidHom.hasCoeToFun.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (Matrix.detMonoidHom.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R], Eq.{max (succ u2) (succ u1)} (forall (a : Matrix.{u1, u1, u2} n n R), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulOneClass.toMul.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (MonoidHom.monoidHomClass.{max u1 u2, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))))) (Matrix.detMonoidHom.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R], Eq.{max (succ u2) (succ u1)} (forall (a : Matrix.{u1, u1, u2} n n R), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Matrix.{u1, u1, u2} n n R) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Matrix.{u1, u1, u2} n n R) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulOneClass.toMul.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (MonoidHom.monoidHomClass.{max u1 u2, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))))) (Matrix.detMonoidHom.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)
 Case conversion may be inaccurate. Consider using '#align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHomₓ'. -/
 @[simp]
 theorem coe_detMonoidHom : (detMonoidHom : Matrix n n R → R) = det :=
@@ -381,7 +381,7 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (σ : Equiv.Perm.{succ u2} n) (M : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (fun (i : n) => M (coeFn.{succ u2, succ u2} (Equiv.Perm.{succ u2} n) (fun (_x : Equiv.{succ u2, succ u2} n n) => n -> n) (Equiv.hasCoeToFun.{succ u2, succ u2} n n) σ i))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) (Units.{0} Int Int.monoid) R (HasLiftT.mk.{1, succ u1} (Units.{0} Int Int.monoid) R (CoeTCₓ.coe.{1, succ u1} (Units.{0} Int Int.monoid) R (coeTrans.{1, 1, succ u1} (Units.{0} Int Int.monoid) Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Units.hasCoe.{0} Int Int.monoid)))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} n) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (σ : Equiv.Perm.{succ u1} n) (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (fun (i : n) => M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ i))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (a : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) a) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (σ : Equiv.Perm.{succ u1} n) (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (fun (i : n) => M (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.Perm.{succ u1} n) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => n) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} n n) σ i))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (a : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) a) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M))
 Case conversion may be inaccurate. Consider using '#align matrix.det_permute Matrix.det_permuteₓ'. -/
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
@@ -393,7 +393,7 @@ theorem det_permute (σ : Perm n) (M : Matrix n n R) :
 lean 3 declaration is
   forall {m : Type.{u2}} {n : Type.{u3}} [_inst_1 : DecidableEq.{succ u3} n] [_inst_2 : Fintype.{u3} n] [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (e : Equiv.{succ u3, succ u2} n m) (A : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.submatrix.{u1, u3, u2, u2, u3} n m m n R A (coeFn.{max 1 (max (succ u3) (succ u2)) (succ u2) (succ u3), max (succ u3) (succ u2)} (Equiv.{succ u3, succ u2} n m) (fun (_x : Equiv.{succ u3, succ u2} n m) => n -> m) (Equiv.hasCoeToFun.{succ u3, succ u2} n m) e) (coeFn.{max 1 (max (succ u3) (succ u2)) (succ u2) (succ u3), max (succ u3) (succ u2)} (Equiv.{succ u3, succ u2} n m) (fun (_x : Equiv.{succ u3, succ u2} n m) => n -> m) (Equiv.hasCoeToFun.{succ u3, succ u2} n m) e))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 A)
 but is expected to have type
-  forall {m : Type.{u1}} {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] (e : Equiv.{succ u2, succ u1} n m) (A : Matrix.{u1, u1, u3} m m R), Eq.{succ u3} R (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n R A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e))) (Matrix.det.{u3, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 A)
+  forall {m : Type.{u1}} {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] (e : Equiv.{succ u2, succ u1} n m) (A : Matrix.{u1, u1, u3} m m R), Eq.{succ u3} R (Matrix.det.{u3, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.submatrix.{u3, u2, u1, u1, u2} n m m n R A (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (Equiv.{succ u2, succ u1} n m) n (fun (_x : n) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n) => m) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} n m) e))) (Matrix.det.{u3, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 A)
 Case conversion may be inaccurate. Consider using '#align matrix.det_submatrix_equiv_self Matrix.det_submatrix_equiv_selfₓ'. -/
 /-- Permuting rows and columns with the same equivalence has no effect. -/
 @[simp]
@@ -413,7 +413,7 @@ theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.subma
 lean 3 declaration is
   forall {m : Type.{u2}} {n : Type.{u3}} [_inst_1 : DecidableEq.{succ u3} n] [_inst_2 : Fintype.{u3} n] [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (e : Equiv.{succ u2, succ u3} m n) (A : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (coeFn.{max 1 (max (succ (max u2 u1)) (succ (max u3 u1))) (succ (max u3 u1)) (succ (max u2 u1)), max (succ (max u2 u1)) (succ (max u3 u1))} (Equiv.{succ (max u2 u1), succ (max u3 u1)} (Matrix.{u2, u2, u1} m m R) (Matrix.{u3, u3, u1} n n R)) (fun (_x : Equiv.{succ (max u2 u1), succ (max u3 u1)} (Matrix.{u2, u2, u1} m m R) (Matrix.{u3, u3, u1} n n R)) => (Matrix.{u2, u2, u1} m m R) -> (Matrix.{u3, u3, u1} n n R)) (Equiv.hasCoeToFun.{succ (max u2 u1), succ (max u3 u1)} (Matrix.{u2, u2, u1} m m R) (Matrix.{u3, u3, u1} n n R)) (Matrix.reindex.{u1, u3, u2, u2, u3} n m m n R e e) A)) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 A)
 but is expected to have type
-  forall {m : Type.{u2}} {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] (e : Equiv.{succ u2, succ u1} m n) (A : Matrix.{u2, u2, u3} m m R), Eq.{succ u3} R (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (Equiv.{max (succ u3) (succ u2), max (succ u3) (succ u1)} (Matrix.{u2, u2, u3} m m R) (Matrix.{u1, u1, u3} n n R)) (Matrix.{u2, u2, u3} m m R) (fun (_x : Matrix.{u2, u2, u3} m m R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Matrix.{u2, u2, u3} m m R) => Matrix.{u1, u1, u3} n n R) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), max (succ u1) (succ u3)} (Matrix.{u2, u2, u3} m m R) (Matrix.{u1, u1, u3} n n R)) (Matrix.reindex.{u3, u1, u2, u2, u1} n m m n R e e) A)) (Matrix.det.{u3, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 A)
+  forall {m : Type.{u2}} {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] (e : Equiv.{succ u2, succ u1} m n) (A : Matrix.{u2, u2, u3} m m R), Eq.{succ u3} R (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (Equiv.{max (succ u3) (succ u2), max (succ u3) (succ u1)} (Matrix.{u2, u2, u3} m m R) (Matrix.{u1, u1, u3} n n R)) (Matrix.{u2, u2, u3} m m R) (fun (_x : Matrix.{u2, u2, u3} m m R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Matrix.{u2, u2, u3} m m R) => Matrix.{u1, u1, u3} n n R) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u3), max (succ u1) (succ u3)} (Matrix.{u2, u2, u3} m m R) (Matrix.{u1, u1, u3} n n R)) (Matrix.reindex.{u3, u1, u2, u2, u1} n m m n R e e) A)) (Matrix.det.{u3, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 A)
 Case conversion may be inaccurate. Consider using '#align matrix.det_reindex_self Matrix.det_reindex_selfₓ'. -/
 /-- Reindexing both indices along the same equivalence preserves the determinant.
 
@@ -428,7 +428,7 @@ theorem det_reindex_self (e : m ≃ n) (A : Matrix m m R) : det (reindex e e A)
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (σ : Equiv.Perm.{succ u2} n), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (PEquiv.toMatrix.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 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_5)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Equiv.toPEquiv.{u2, u2} n n σ))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) (Units.{0} Int Int.monoid) R (HasLiftT.mk.{1, succ u1} (Units.{0} Int Int.monoid) R (CoeTCₓ.coe.{1, succ u1} (Units.{0} Int Int.monoid) R (coeTrans.{1, 1, succ u1} (Units.{0} Int Int.monoid) Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Units.hasCoe.{0} Int Int.monoid)))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} n) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (σ : Equiv.Perm.{succ u1} n), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (PEquiv.toMatrix.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Equiv.toPEquiv.{u1, u1} n n σ))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (a : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) a) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (σ : Equiv.Perm.{succ u1} n), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (PEquiv.toMatrix.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Equiv.toPEquiv.{u1, u1} n n σ))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (a : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) a) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_permutation Matrix.det_permutationₓ'. -/
 /-- The determinant of a permutation matrix equals its sign. -/
 @[simp]
@@ -490,7 +490,7 @@ theorem det_neg_eq_smul (A : Matrix n n R) : det (-A) = (-1 : Units ℤ) ^ Finty
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (v : n -> R) (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (coeFn.{max 1 (max (max (succ u2) (succ u1)) (succ (max u2 u1))) (succ (max u2 u1)) (succ u2) (succ u1), max (max (succ u2) (succ u1)) (succ (max u2 u1))} (Equiv.{max (succ u2) (succ u1), succ (max u2 u1)} (n -> n -> R) (Matrix.{u2, u2, u1} n n R)) (fun (_x : Equiv.{max (succ u2) (succ u1), succ (max u2 u1)} (n -> n -> R) (Matrix.{u2, u2, u1} n n R)) => (n -> n -> R) -> (Matrix.{u2, u2, u1} n n R)) (Equiv.hasCoeToFun.{max (succ u2) (succ u1), succ (max u2 u1)} (n -> n -> R) (Matrix.{u2, u2, u1} n n R)) (Matrix.of.{u1, u2, u2} n n R) (fun (i : n) (j : n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (v j) (A i j)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Finset.prod.{u1, u2} R n (CommRing.toCommMonoid.{u1} R _inst_5) (Finset.univ.{u2} n _inst_2) (fun (i : n) => v i)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (v : n -> R) (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (n -> n -> R) (fun (_x : n -> n -> R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n -> n -> R) => Matrix.{u1, u1, u2} n n R) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (Matrix.of.{u2, u1, u1} n n R) (fun (i : n) (j : n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (v j) (A i j)))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => v i)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (v : n -> R) (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (n -> n -> R) (fun (_x : n -> n -> R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n -> n -> R) => Matrix.{u1, u1, u2} n n R) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (Matrix.of.{u2, u1, u1} n n R) (fun (i : n) (j : n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (v j) (A i j)))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => v i)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_mul_row Matrix.det_mul_rowₓ'. -/
 /-- Multiplying each row by a fixed `v i` multiplies the determinant by
 the product of the `v`s. -/
@@ -509,7 +509,7 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (v : n -> R) (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (coeFn.{max 1 (max (max (succ u2) (succ u1)) (succ (max u2 u1))) (succ (max u2 u1)) (succ u2) (succ u1), max (max (succ u2) (succ u1)) (succ (max u2 u1))} (Equiv.{max (succ u2) (succ u1), succ (max u2 u1)} (n -> n -> R) (Matrix.{u2, u2, u1} n n R)) (fun (_x : Equiv.{max (succ u2) (succ u1), succ (max u2 u1)} (n -> n -> R) (Matrix.{u2, u2, u1} n n R)) => (n -> n -> R) -> (Matrix.{u2, u2, u1} n n R)) (Equiv.hasCoeToFun.{max (succ u2) (succ u1), succ (max u2 u1)} (n -> n -> R) (Matrix.{u2, u2, u1} n n R)) (Matrix.of.{u1, u2, u2} n n R) (fun (i : n) (j : n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (v i) (A i j)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Finset.prod.{u1, u2} R n (CommRing.toCommMonoid.{u1} R _inst_5) (Finset.univ.{u2} n _inst_2) (fun (i : n) => v i)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (v : n -> R) (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (n -> n -> R) (fun (_x : n -> n -> R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : n -> n -> R) => Matrix.{u1, u1, u2} n n R) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (Matrix.of.{u2, u1, u1} n n R) (fun (i : n) (j : n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (v i) (A i j)))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => v i)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (v : n -> R) (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (n -> n -> R) (fun (_x : n -> n -> R) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : n -> n -> R) => Matrix.{u1, u1, u2} n n R) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (n -> n -> R) (Matrix.{u1, u1, u2} n n R)) (Matrix.of.{u2, u1, u1} n n R) (fun (i : n) (j : n) => HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (v i) (A i j)))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Finset.prod.{u2, u1} R n (CommRing.toCommMonoid.{u2} R _inst_5) (Finset.univ.{u1} n _inst_2) (fun (i : n) => v i)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_mul_column Matrix.det_mul_columnₓ'. -/
 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
 the product of the `v`s. -/
@@ -537,7 +537,7 @@ variable {S : Type w} [CommRing S]
 lean 3 declaration is
   forall {n : Type.{u3}} [_inst_1 : DecidableEq.{succ u3} n] [_inst_2 : Fintype.{u3} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (M : Matrix.{u3, u3, u1} n n R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) f (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.nonAssocSemiring.{u1, u3} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u2, u3} n S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.nonAssocSemiring.{u1, u3} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u2, u3} n S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) => (Matrix.{u3, u3, u1} n n R) -> (Matrix.{u3, u3, u2} n n S)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.nonAssocSemiring.{u1, u3} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u2, u3} n S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (RingHom.mapMatrix.{u1, u2, u3} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) f (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => Matrix.{u1, u1, u3} n n S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (RingHom.instRingHomClassRingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (RingHom.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) f (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Matrix.{u1, u1, u2} n n R) => Matrix.{u1, u1, u3} n n S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (RingHom.instRingHomClassRingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (RingHom.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) f) M))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_det RingHom.map_detₓ'. -/
 theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
@@ -866,7 +866,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} (k : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (c : (Fin n) -> R), (forall (i : Fin n), (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLt (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) k (Fin.succ n i)) -> (Eq.{succ u1} R (c i) (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_5))))))))))) -> (forall {M : Matrix.{0, 0, u1} (Fin (Nat.succ n)) (Fin (Nat.succ n)) R} {N : Matrix.{0, 0, u1} (Fin (Nat.succ n)) (Fin (Nat.succ n)) R}, (forall (j : Fin (Nat.succ n)), Eq.{succ u1} R (M (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (OfNat.mk.{0} (Fin (Nat.succ n)) 0 (Zero.zero.{0} (Fin (Nat.succ n)) (Fin.hasZeroOfNeZero (Nat.succ n) (NeZero.succ n))))) j) (N (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (OfNat.mk.{0} (Fin (Nat.succ n)) 0 (Zero.zero.{0} (Fin (Nat.succ n)) (Fin.hasZeroOfNeZero (Nat.succ n) (NeZero.succ n))))) j)) -> (forall (i : Fin n) (j : Fin (Nat.succ n)), Eq.{succ u1} R (M (Fin.succ n i) j) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (N (Fin.succ n i) j) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (c i) (M (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) j)))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (Nat.succ n)) (fun (a : Fin (Nat.succ n)) (b : Fin (Nat.succ n)) => Fin.decidableEq (Nat.succ n) a b) (Fin.fintype (Nat.succ n)) R _inst_5 M) (Matrix.det.{u1, 0} (Fin (Nat.succ n)) (fun (a : Fin (Nat.succ n)) (b : Fin (Nat.succ n)) => Fin.decidableEq (Nat.succ n) a b) (Fin.fintype (Nat.succ n)) R _inst_5 N)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} (k : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (c : (Fin n) -> R), (forall (i : Fin n), (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) k (Fin.succ n i)) -> (Eq.{succ u1} R (c i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) -> (forall {M : Matrix.{0, 0, u1} (Fin (Nat.succ n)) (Fin (Nat.succ n)) R} {N : Matrix.{0, 0, u1} (Fin (Nat.succ n)) (Fin (Nat.succ n)) R}, (forall (j : Fin (Nat.succ n)), Eq.{succ u1} R (M (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n))) j) (N (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n))) j)) -> (forall (i : Fin n) (j : Fin (Nat.succ n)), Eq.{succ u1} R (M (Fin.succ n i) j) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (N (Fin.succ n i) j) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (c i) (M (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin n) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n)) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin n) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc n) i) j)))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (Nat.succ n)) (fun (a : Fin (Nat.succ n)) (b : Fin (Nat.succ n)) => instDecidableEqFin (Nat.succ n) a b) (Fin.fintype (Nat.succ n)) R _inst_5 M) (Matrix.det.{u1, 0} (Fin (Nat.succ n)) (fun (a : Fin (Nat.succ n)) (b : Fin (Nat.succ n)) => instDecidableEqFin (Nat.succ n) a b) (Fin.fintype (Nat.succ n)) R _inst_5 N)))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} (k : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (c : (Fin n) -> R), (forall (i : Fin n), (LT.lt.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLTFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) k (Fin.succ n i)) -> (Eq.{succ u1} R (c i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))))) -> (forall {M : Matrix.{0, 0, u1} (Fin (Nat.succ n)) (Fin (Nat.succ n)) R} {N : Matrix.{0, 0, u1} (Fin (Nat.succ n)) (Fin (Nat.succ n)) R}, (forall (j : Fin (Nat.succ n)), Eq.{succ u1} R (M (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n))) j) (N (OfNat.ofNat.{0} (Fin (Nat.succ n)) 0 (Fin.instOfNatFin (Nat.succ n) 0 (NeZero.succ n))) j)) -> (forall (i : Fin n) (j : Fin (Nat.succ n)), Eq.{succ u1} R (M (Fin.succ n i) j) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (N (Fin.succ n i) j) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (c i) (M (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin n) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n)) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin n) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc n) i) j)))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (Nat.succ n)) (fun (a : Fin (Nat.succ n)) (b : Fin (Nat.succ n)) => instDecidableEqFin (Nat.succ n) a b) (Fin.fintype (Nat.succ n)) R _inst_5 M) (Matrix.det.{u1, 0} (Fin (Nat.succ n)) (fun (a : Fin (Nat.succ n)) (b : Fin (Nat.succ n)) => instDecidableEqFin (Nat.succ n) a b) (Fin.fintype (Nat.succ n)) R _inst_5 N)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_auxₓ'. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (hc : ∀ i : Fin n, k < i.succ → c i = 0)
@@ -911,7 +911,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} {A : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R} {B : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R} (c : (Fin n) -> R), (forall (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u1} R (A (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) j) (B (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))) j)) -> (forall (i : Fin n) (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u1} R (A (Fin.succ n i) j) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (B (Fin.succ n i) j) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (c i) (A (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) => (Fin n) -> (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (RelEmbedding.hasCoeToFun.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (Fin.castSucc n) i) j)))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Fin.decidableEq (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_5 A) (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) => Fin.decidableEq (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R _inst_5 B))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} {A : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R} {B : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R} (c : (Fin n) -> R), (forall (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} R (A (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) j) (B (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) j)) -> (forall (i : Fin n) (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} R (A (Fin.succ n i) j) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (B (Fin.succ n i) j) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (c i) (A (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin n) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n)) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin n) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) (Fin.castSucc n) i) j)))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 A) (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 B))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} {A : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R} {B : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R} (c : (Fin n) -> R), (forall (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} R (A (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) j) (B (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) 0 (Fin.instOfNatFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (NeZero.succ n))) j)) -> (forall (i : Fin n) (j : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))), Eq.{succ u1} R (A (Fin.succ n i) j) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (B (Fin.succ n i) j) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (c i) (A (FunLike.coe.{1, 1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (fun (_x : Fin n) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Fin n) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (InfHomClass.toFunLike.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Lattice.toInf.{0} (Fin n) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n)))) (Lattice.toInf.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n)) (LatticeHomClass.toInfHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (DistribLattice.toLattice.{0} (Fin n) (instDistribLattice.{0} (Fin n) (Fin.instLinearOrderFin n))) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (OrderHomClass.toLatticeHomClass.{0, 0, 0} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin n) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc n) i) j)))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 A) (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 B))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
@@ -925,7 +925,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {n : Nat} {A : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R} {B : Matrix.{0, 0, u1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) R} (c : (Fin n) -> R), (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))), Eq.{succ u1} R (A i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n)))))) (B i (OfNat.ofNat.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)) (NeZero.succ n))))))) -> (forall (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (j : Fin n), Eq.{succ u1} R (A i (Fin.succ n j)) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (B i (Fin.succ n j)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (c j) (A i (coeFn.{1, 1} (OrderEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Fin.hasLe n) (Fin.hasLe (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (fun (_x : RelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (LE.le.{0} (Fin n) (Fin.hasLe n)) (LE.le.{0} (Fin 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 but is expected to have type
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Nat 1 (instOfNatNat 1)))) (instLEFin n) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.instLinearOrderFin n) (Fin.instLatticeFinHAddNatInstHAddInstAddNatOfNat n) (RelEmbedding.instRelHomClassRelEmbedding.{0, 0} (Fin n) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Fin n) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Fin n) => LE.le.{0} (Fin n) (instLEFin n) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LE.le.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (instLEFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) (Fin.castSucc n) j))))) -> (Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 A) (Matrix.det.{u1, 0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (b : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => instDecidableEqFin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a b) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) R _inst_5 B))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_col_eq_smul_add_pred Matrix.det_eq_of_forall_col_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}

86d1873c

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -675,7 +675,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5013 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.4948 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_smul Matrix.det_updateRow_smulₓ'. -/
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
@@ -686,7 +686,7 @@ theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5085 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5019 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul Matrix.det_updateColumn_smulₓ'. -/
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=

86d1873c

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -134,7 +134,7 @@ theorem det_zero (h : Nonempty n) : det (0 : Matrix n n R) = 0 :=
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R], Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (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_1 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_5)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))))))) (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_5))))))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R], Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (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_1 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R], Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (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_1 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_one Matrix.det_oneₓ'. -/
 @[simp]
 theorem det_one : det (1 : Matrix n n R) = 1 := by rw [← diagonal_one] <;> simp [-diagonal_one]
@@ -144,7 +144,7 @@ theorem det_one : det (1 : Matrix n n R) = 1 := by rw [← diagonal_one] <;> sim
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsEmpty.{succ u2} n] {A : Matrix.{u2, u2, u1} n n R}, Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (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_5))))))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : IsEmpty.{succ u1} n] {A : Matrix.{u1, u1, u2} n n R}, Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : IsEmpty.{succ u1} n] {A : Matrix.{u1, u1, u2} n n R}, Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_is_empty Matrix.det_isEmptyₓ'. -/
 theorem det_isEmpty [IsEmpty n] {A : Matrix n n R} : det A = 1 := by simp [det_apply]
 #align matrix.det_is_empty Matrix.det_isEmpty
@@ -153,7 +153,7 @@ theorem det_isEmpty [IsEmpty n] {A : Matrix n n R} : det A = 1 := by simp [det_a
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsEmpty.{succ u2} n], Eq.{max (succ (max u2 u1)) (succ u1)} ((Matrix.{u2, u2, u1} n n R) -> R) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5) (Function.const.{succ u1, succ (max u2 u1)} R (Matrix.{u2, u2, u1} n n R) (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_5)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : IsEmpty.{succ u1} n], Eq.{max (succ u2) (succ u1)} ((Matrix.{u1, u1, u2} n n R) -> R) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5) (Function.const.{succ u2, max (succ u2) (succ u1)} R (Matrix.{u1, u1, u2} n n R) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : IsEmpty.{succ u1} n], Eq.{max (succ u2) (succ u1)} ((Matrix.{u1, u1, u2} n n R) -> R) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5) (Function.const.{succ u2, max (succ u2) (succ u1)} R (Matrix.{u1, u1, u2} n n R) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align matrix.coe_det_is_empty Matrix.coe_det_isEmptyₓ'. -/
 @[simp]
 theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.const _ 1 :=
@@ -166,7 +166,7 @@ theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.cons
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n n R}, (Eq.{1} Nat (Fintype.card.{u2} n _inst_2) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (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_5)))))))))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R}, (Eq.{1} Nat (Fintype.card.{u1} n _inst_2) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R}, (Eq.{1} Nat (Fintype.card.{u1} n _inst_2) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_one_of_card_eq_zero Matrix.det_eq_one_of_card_eq_zeroₓ'. -/
 theorem det_eq_one_of_card_eq_zero {A : Matrix n n R} (h : Fintype.card n = 0) : det A = 1 :=
   haveI : IsEmpty n := fintype.card_eq_zero_iff.mp h
@@ -295,7 +295,7 @@ def detMonoidHom : Matrix n n R →* R where
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R], Eq.{max (succ (max u2 u1)) (succ u1)} ((fun (_x : MonoidHom.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) => (Matrix.{u2, u2, u1} n n R) -> R) (Matrix.detMonoidHom.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ (max u2 u1)) (succ u1)} (MonoidHom.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (fun (_x : MonoidHom.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) => (Matrix.{u2, u2, u1} n n R) -> R) (MonoidHom.hasCoeToFun.{max u2 u1, u1} (Matrix.{u2, u2, u1} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.nonAssocSemiring.{u1, u2} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (Matrix.detMonoidHom.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R], Eq.{max (succ u2) (succ u1)} (forall (a : Matrix.{u1, u1, u2} n n R), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulOneClass.toMul.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (MonoidHom.monoidHomClass.{max u1 u2, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))))) (Matrix.detMonoidHom.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R], Eq.{max (succ u2) (succ u1)} (forall (a : Matrix.{u1, u1, u2} n n R), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => R) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulOneClass.toMul.{max u1 u2} (Matrix.{u1, u1, u2} n n R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (MulOneClass.toMul.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u2} (MonoidHom.{max u2 u1, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (MonoidHom.monoidHomClass.{max u1 u2, u2} (Matrix.{u1, u1, u2} n n R) R (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))))) (Matrix.detMonoidHom.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5)
 Case conversion may be inaccurate. Consider using '#align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHomₓ'. -/
 @[simp]
 theorem coe_detMonoidHom : (detMonoidHom : Matrix n n R → R) = det :=
@@ -339,7 +339,7 @@ theorem det_mul_right_comm (M N P : Matrix m m R) : det (M ⬝ N ⬝ P) = det (M
 lean 3 declaration is
   forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (N : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) M) N) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Units.hasInv.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) M)))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 but is expected to have type
-  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInv.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInv.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 Case conversion may be inaccurate. Consider using '#align matrix.det_units_conj Matrix.det_units_conjₓ'. -/
 theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M ⬝ N ⬝ ↑M⁻¹ : Matrix m m R) = det N := by
@@ -350,7 +350,7 @@ theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
 lean 3 declaration is
   forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (N : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Units.hasInv.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) M)) N) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) M))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 but is expected to have type
-  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInv.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInv.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 Case conversion may be inaccurate. Consider using '#align matrix.det_units_conj' Matrix.det_units_conj'ₓ'. -/
 theorem det_units_conj' (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M⁻¹ ⬝ N ⬝ ↑M : Matrix m m R) = det N :=
@@ -428,7 +428,7 @@ theorem det_reindex_self (e : m ≃ n) (A : Matrix m m R) : det (reindex e e A)
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (σ : Equiv.Perm.{succ u2} n), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (PEquiv.toMatrix.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 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_5)))))) (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Equiv.toPEquiv.{u2, u2} n n σ))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) (Units.{0} Int Int.monoid) R (HasLiftT.mk.{1, succ u1} (Units.{0} Int Int.monoid) R (CoeTCₓ.coe.{1, succ u1} (Units.{0} Int Int.monoid) R (coeTrans.{1, 1, succ u1} (Units.{0} Int Int.monoid) Int R (Int.castCoe.{u1} R (AddGroupWithOne.toHasIntCast.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Units.hasCoe.{0} Int Int.monoid)))) (coeFn.{succ u2, succ u2} (MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (fun (_x : MonoidHom.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) => (Equiv.Perm.{succ u2} n) -> (Units.{0} Int Int.monoid)) (MonoidHom.hasCoeToFun.{u2, 0} (Equiv.Perm.{succ u2} n) (Units.{0} Int Int.monoid) (Monoid.toMulOneClass.{u2} (Equiv.Perm.{succ u2} n) (DivInvMonoid.toMonoid.{u2} (Equiv.Perm.{succ u2} n) (Group.toDivInvMonoid.{u2} (Equiv.Perm.{succ u2} n) (Equiv.Perm.permGroup.{u2} n)))) (Units.mulOneClass.{0} Int Int.monoid)) (Equiv.Perm.sign.{u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (σ : Equiv.Perm.{succ u1} n), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (PEquiv.toMatrix.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (Equiv.toPEquiv.{u1, u1} n n σ))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (a : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) a) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (σ : Equiv.Perm.{succ u1} n), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (PEquiv.toMatrix.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Equiv.toPEquiv.{u1, u1} n n σ))) (Int.cast.{u2} R (Ring.toIntCast.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Units.val.{0} Int Int.instMonoidInt (FunLike.coe.{succ u1, succ u1, 1} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (fun (a : Equiv.Perm.{succ u1} n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Equiv.Perm.{succ u1} n) => Units.{0} Int Int.instMonoidInt) a) (MulHomClass.toFunLike.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (MulOneClass.toMul.{u1} (Equiv.Perm.{succ u1} n) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n))))) (MulOneClass.toMul.{0} (Units.{0} Int Int.instMonoidInt) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (MonoidHomClass.toMulHomClass.{u1, u1, 0} (MonoidHom.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)) (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt) (MonoidHom.monoidHomClass.{u1, 0} (Equiv.Perm.{succ u1} n) (Units.{0} Int Int.instMonoidInt) (Monoid.toMulOneClass.{u1} (Equiv.Perm.{succ u1} n) (DivInvMonoid.toMonoid.{u1} (Equiv.Perm.{succ u1} n) (Group.toDivInvMonoid.{u1} (Equiv.Perm.{succ u1} n) (Equiv.Perm.permGroup.{u1} n)))) (Units.instMulOneClassUnits.{0} Int Int.instMonoidInt)))) (Equiv.Perm.sign.{u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2) σ)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_permutation Matrix.det_permutationₓ'. -/
 /-- The determinant of a permutation matrix equals its sign. -/
 @[simp]
@@ -442,7 +442,7 @@ theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matri
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n n R) (c : R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (SMul.smul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.hasSmul.{u1, u2, u2, u1} n n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))))) c A)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_5)))) c (Fintype.card.{u2} n _inst_2)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R) (c : R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u2, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) c A)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) c (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R) (c : R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u2, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) c A)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) c (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul Matrix.det_smulₓ'. -/
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
@@ -456,7 +456,7 @@ theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {α : Type.{u3}} [_inst_6 : Monoid.{u3} α] [_inst_7 : DistribMulAction.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))] [_inst_8 : IsScalarTower.{u3, u1, u1} α R R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7)))] [_inst_9 : SMulCommClass.{u3, u1, u1} α R R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))))] (c : α) (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (SMul.smul.{u3, max u2 u1} α (Matrix.{u2, u2, u1} n n R) (Matrix.hasSmul.{u1, u2, u2, u3} n n α R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7)))) c A)) (SMul.smul.{u3, u1} α R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7))) (HPow.hPow.{u3, 0, u3} α Nat α (instHPow.{u3, 0} α Nat (Monoid.Pow.{u3} α _inst_6)) c (Fintype.card.{u2} n _inst_2)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] {α : Type.{u2}} [_inst_6 : Monoid.{u2} α] [_inst_7 : DistribMulAction.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))] [_inst_8 : IsScalarTower.{u2, u3, u3} α R R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))) (Algebra.toSMul.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_5) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_5)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7)))] [_inst_9 : SMulCommClass.{u2, u3, u3} α R R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))) (Algebra.toSMul.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_5) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_5)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5)))] (c : α) (A : Matrix.{u1, u1, u3} n n R), Eq.{succ u3} R (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (HSMul.hSMul.{u2, max u3 u1, max u3 u1} α (Matrix.{u1, u1, u3} n n R) (Matrix.{u1, u1, u3} n n R) (instHSMul.{u2, max u3 u1} α (Matrix.{u1, u1, u3} n n R) (Matrix.smul.{u3, u1, u1, u2} n n α R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))))) c A)) (HSMul.hSMul.{u2, u3, u3} α R R (instHSMul.{u2, u3} α R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α _inst_6)) c (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] {α : Type.{u2}} [_inst_6 : Monoid.{u2} α] [_inst_7 : DistribMulAction.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))] [_inst_8 : IsScalarTower.{u2, u3, u3} α R R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))) (Algebra.toSMul.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7)))] [_inst_9 : SMulCommClass.{u2, u3, u3} α R R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))) (Algebra.toSMul.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5)))] (c : α) (A : Matrix.{u1, u1, u3} n n R), Eq.{succ u3} R (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (HSMul.hSMul.{u2, max u3 u1, max u3 u1} α (Matrix.{u1, u1, u3} n n R) (Matrix.{u1, u1, u3} n n R) (instHSMul.{u2, max u3 u1} α (Matrix.{u1, u1, u3} n n R) (Matrix.smul.{u3, u1, u1, u2} n n α R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))))) c A)) (HSMul.hSMul.{u2, u3, u3} α R R (instHSMul.{u2, u3} α R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α _inst_6)) c (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_smul_of_tower Matrix.det_smul_of_towerₓ'. -/
 @[simp]
 theorem det_smul_of_tower {α} [Monoid α] [DistribMulAction α R] [IsScalarTower α R R]
@@ -468,7 +468,7 @@ theorem det_smul_of_tower {α} [Monoid α] [DistribMulAction α R] [IsScalarTowe
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.hasNeg.{u1, u2, u2} n n R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) A)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Neg.neg.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (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_5))))))))) (Fintype.card.{u2} n _inst_2)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Neg.neg.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.neg.{u2, u1, u1} n n R (Ring.toNeg.{u2} R (CommRing.toRing.{u2} R _inst_5))) A)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Neg.neg.{u2} R (Ring.toNeg.{u2} R (CommRing.toRing.{u2} R _inst_5)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Neg.neg.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.neg.{u2, u1, u1} n n R (Ring.toNeg.{u2} R (CommRing.toRing.{u2} R _inst_5))) A)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Neg.neg.{u2} R (Ring.toNeg.{u2} R (CommRing.toRing.{u2} R _inst_5)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_neg Matrix.det_negₓ'. -/
 theorem det_neg (A : Matrix n n R) : det (-A) = (-1) ^ Fintype.card n * det A := by
   rw [← det_smul, neg_one_smul]
@@ -522,7 +522,7 @@ theorem det_mul_column (v : n → R) (A : Matrix n n R) :
 lean 3 declaration is
   forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} m m R) (n : Nat), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} m m R) Nat (Matrix.{u2, u2, u1} m m R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} m m R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))) M n)) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M) n)
 but is expected to have type
-  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} m m R) (n : Nat), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u1, u1, u2} m m R) Nat (Matrix.{u1, u1, u2} m m R) (instHPow.{max u2 u1, 0} (Matrix.{u1, u1, u2} m m R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))))) M n)) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M) n)
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} m m R) (n : Nat), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u1, u1, u2} m m R) Nat (Matrix.{u1, u1, u2} m m R) (instHPow.{max u2 u1, 0} (Matrix.{u1, u1, u2} m m R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))))) M n)) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M) n)
 Case conversion may be inaccurate. Consider using '#align matrix.det_pow Matrix.det_powₓ'. -/
 @[simp]
 theorem det_pow (M : Matrix m m R) (n : ℕ) : det (M ^ n) = det M ^ n :=
@@ -537,7 +537,7 @@ variable {S : Type w} [CommRing S]
 lean 3 declaration is
   forall {n : Type.{u3}} [_inst_1 : DecidableEq.{succ u3} n] [_inst_2 : Fintype.{u3} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (M : Matrix.{u3, u3, u1} n n R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))) f (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingHom.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.nonAssocSemiring.{u1, u3} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u2, u3} n S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (fun (_x : RingHom.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.nonAssocSemiring.{u1, u3} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u2, u3} n S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) => (Matrix.{u3, u3, u1} n n R) -> (Matrix.{u3, u3, u2} n n S)) (RingHom.hasCoeToFun.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.nonAssocSemiring.{u1, u3} n R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u2, u3} n S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (RingHom.mapMatrix.{u1, u2, u3} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] (f : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) f (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => Matrix.{u1, u1, u3} n n S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (RingHom.instRingHomClassRingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (RingHom.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] (f : RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (M : Matrix.{u1, u1, u2} n n R), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) f (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (fun (_x : Matrix.{u1, u1, u2} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Matrix.{u1, u1, u2} n n R) => Matrix.{u1, u1, u3} n n S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (RingHom.instRingHomClassRingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (RingHom.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) f) M))
 Case conversion may be inaccurate. Consider using '#align ring_hom.map_det RingHom.map_detₓ'. -/
 theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
@@ -547,7 +547,7 @@ theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.de
 lean 3 declaration is
   forall {n : Type.{u3}} [_inst_1 : DecidableEq.{succ u3} n] [_inst_2 : Fintype.{u3} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] (f : RingEquiv.{u1, u2} R S (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6))) (Distrib.toHasAdd.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (M : Matrix.{u3, u3, u1} n n R), Eq.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingEquiv.{u1, u2} R S (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6))) (Distrib.toHasAdd.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) (fun (_x : RingEquiv.{u1, u2} R S (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6))) (Distrib.toHasAdd.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) => R -> S) (RingEquiv.hasCoeToFun.{u1, u2} R S (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Distrib.toHasMul.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6))) (Distrib.toHasAdd.{u2} S (Ring.toDistrib.{u2} S (CommRing.toRing.{u2} S _inst_6)))) f (Matrix.det.{u1, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 M)) (Matrix.det.{u2, u3} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 (coeFn.{max (succ (max u3 u1)) (succ (max u3 u2)), max (succ (max u3 u1)) (succ (max u3 u2))} (RingEquiv.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.hasMul.{u1, u3} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (Matrix.hasAdd.{u1, u3, u3} n n R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (Matrix.hasMul.{u2, u3} n S _inst_2 (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (Matrix.hasAdd.{u2, u3, u3} n n S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))))) (fun (_x : RingEquiv.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.hasMul.{u1, u3} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (Matrix.hasAdd.{u1, u3, u3} n n R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (Matrix.hasMul.{u2, u3} n S _inst_2 (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (Matrix.hasAdd.{u2, u3, u3} n n S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))))) => (Matrix.{u3, u3, u1} n n R) -> (Matrix.{u3, u3, u2} n n S)) (RingEquiv.hasCoeToFun.{max u3 u1, max u3 u2} (Matrix.{u3, u3, u1} n n R) (Matrix.{u3, u3, u2} n n S) (Matrix.hasMul.{u1, u3} n R _inst_2 (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (Matrix.hasAdd.{u1, u3, u3} n n R (Distrib.toHasAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (Matrix.hasMul.{u2, u3} n S _inst_2 (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))) (Matrix.hasAdd.{u2, u3, u3} n n S (Distrib.toHasAdd.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6)))))))) (RingEquiv.mapMatrix.{u1, u2, u3} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_6))) f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] (f : RingEquiv.{u2, u3} R S (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocRing.toMul.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (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_5)))))) (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (M : Matrix.{u1, u1, u2} n n R), 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(CommRing.toRing.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (RingEquiv.instRingEquivClassRingEquiv.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))))))))))) (RingEquiv.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] (f : RingEquiv.{u2, u3} R S (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocRing.toMul.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (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_5)))))) (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (M : Matrix.{u1, u1, u2} n n R), 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (EquivLike.toEmbeddingLike.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u1), max (succ u3) (succ u1)} (RingEquiv.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (MulEquivClass.toEquivLike.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingEquiv.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (RingEquivClass.toMulEquivClass.{max (max u2 u3) u1, max u2 u1, max u3 u1} (RingEquiv.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))))) (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (RingEquiv.instRingEquivClassRingEquiv.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.instMulMatrix.{u2, u1} n R _inst_2 (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))))))))) (RingEquiv.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))) (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))) f) M))
 Case conversion may be inaccurate. Consider using '#align ring_equiv.map_det RingEquiv.map_detₓ'. -/
 theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
@@ -557,7 +557,7 @@ theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.
 lean 3 declaration is
   forall {n : Type.{u4}} [_inst_1 : DecidableEq.{succ u4} n] [_inst_2 : Fintype.{u4} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] {T : Type.{u3}} [_inst_8 : CommRing.{u3} T] [_inst_9 : Algebra.{u1, u3} R T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8))] (f : AlgHom.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u4, u4, u2} n n S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (fun (_x : AlgHom.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) => S -> T) ([anonymous].{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) f (Matrix.det.{u2, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u3, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (coeFn.{max (succ (max u4 u2)) (succ (max u4 u3)), max (succ (max u4 u2)) (succ (max u4 u3))} (AlgHom.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (fun (_x : AlgHom.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) => (Matrix.{u4, u4, u2} n n S) -> (Matrix.{u4, u4, u3} n n T)) ([anonymous].{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (AlgHom.mapMatrix.{u2, u3, u4, u1} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9 f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))] (f : AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) (AlgHom.algHomClass.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (Matrix.{u1, u1, u3} n n S) (fun (_x : Matrix.{u1, u1, u3} n n S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u1, u1, u3} n n S) => Matrix.{u1, u1, u4} n n T) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (SMulZeroClass.toSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)))))) (SMulZeroClass.toSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toZero.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toAddZeroClass.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9) (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (AlgHom.algHomClass.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)))))) (AlgHom.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))] (f : AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgHom.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R 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(Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.algHomClass.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)))))) (AlgHom.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
 Case conversion may be inaccurate. Consider using '#align alg_hom.map_det AlgHom.map_detₓ'. -/
 theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S →ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
@@ -568,7 +568,7 @@ theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f
 lean 3 declaration is
   forall {n : Type.{u4}} [_inst_1 : DecidableEq.{succ u4} n] [_inst_2 : Fintype.{u4} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {S : Type.{u2}} [_inst_6 : CommRing.{u2} S] [_inst_7 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6))] {T : Type.{u3}} [_inst_8 : CommRing.{u3} T] [_inst_9 : Algebra.{u1, u3} R T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8))] (f : AlgEquiv.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u4, u4, u2} n n S), Eq.{succ u3} T (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgEquiv.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) (fun (_x : AlgEquiv.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) => S -> T) (AlgEquiv.hasCoeToFun.{u1, u2, u3} R S T (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9) f (Matrix.det.{u2, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u3, u4} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (coeFn.{max (succ (max u4 u2)) (succ (max u4 u3)), max (succ (max u4 u2)) (succ (max u4 u3))} (AlgEquiv.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (fun (_x : AlgEquiv.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) => (Matrix.{u4, u4, u2} n n S) -> (Matrix.{u4, u4, u3} n n T)) (AlgEquiv.hasCoeToFun.{u1, max u4 u2, max u4 u3} R (Matrix.{u4, u4, u2} n n S) (Matrix.{u4, u4, u3} n n T) (CommRing.toCommSemiring.{u1} R _inst_5) (Matrix.semiring.{u2, u4} n S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u3, u4} n T (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.algebra.{u2, u4, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) _inst_7) (Matrix.algebra.{u3, u4, u1} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_9)) (AlgEquiv.mapMatrix.{u2, u3, u4, u1} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u1} R _inst_5) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_6)) (Ring.toSemiring.{u3} T (CommRing.toRing.{u3} T _inst_8)) _inst_7 _inst_9 f) M))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))] (f : AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9)))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (Matrix.{u1, u1, u3} n n S) (fun (_x : Matrix.{u1, u1, u3} n n S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u1, u1, u3} n n S) => Matrix.{u1, u1, u4} n n T) _x) (SMulHomClass.toFunLike.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (SMulZeroClass.toSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)))))) (SMulZeroClass.toSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toZero.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toAddZeroClass.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9) (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (AlgEquivClass.toAlgHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))))))) (AlgEquiv.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {S : Type.{u3}} [_inst_6 : CommRing.{u3} S] [_inst_7 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))] {T : Type.{u4}} [_inst_8 : CommRing.{u4} T] [_inst_9 : Algebra.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))] (f : AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (M : Matrix.{u1, u1, u3} n n S), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : S) => T) _x) (SMulHomClass.toFunLike.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (SMulZeroClass.toSMul.{u2, u3} R S (AddMonoid.toZero.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u3} R S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u3} R S (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))))) (SMulZeroClass.toSMul.{u2, u4} R T (AddMonoid.toZero.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribSMul.toSMulZeroClass.{u2, u4} R T (AddMonoid.toAddZeroClass.{u4} T (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))))) (DistribMulAction.toDistribSMul.{u2, u4} R T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9) R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9)))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T 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(Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T 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n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) (AlgEquivClass.toAlgHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_9))))))) (AlgEquiv.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_6)) (CommSemiring.toSemiring.{u4} T (CommRing.toCommSemiring.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
 Case conversion may be inaccurate. Consider using '#align alg_equiv.map_det AlgEquiv.map_detₓ'. -/
 theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S ≃ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
@@ -581,7 +581,7 @@ end HomMap
 lean 3 declaration is
   forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5)))] (M : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.conjTranspose.{u1, u2, u2} m m R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5))) _inst_6))) M)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5))) _inst_6))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M))
 but is expected to have type
-  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : StarRing.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5)))] (M : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.conjTranspose.{u2, u1, u1} m m R (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5))) _inst_6))) M)) (Star.star.{u2} R (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5))) _inst_6))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M))
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5)))] (M : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.conjTranspose.{u2, u1, u1} m m R (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5))) _inst_6))) M)) (Star.star.{u2} R (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5))) _inst_6))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M))
 Case conversion may be inaccurate. Consider using '#align matrix.det_conj_transpose Matrix.det_conjTransposeₓ'. -/
 @[simp]
 theorem det_conjTranspose [StarRing R] (M : Matrix m m R) : det Mᴴ = star (det M) :=
@@ -675,7 +675,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5007 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5013 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_smul Matrix.det_updateRow_smulₓ'. -/
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
@@ -686,7 +686,7 @@ theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5079 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5085 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul Matrix.det_updateColumn_smulₓ'. -/
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=
@@ -699,7 +699,7 @@ theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) (SMul.smul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.hasSmul.{u1, u2, u2, u1} n n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))))) s M) j u)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} n _inst_2) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u2, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s M) j u)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u1} n _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u2, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s M) j u)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u1} n _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_smul' Matrix.det_updateRow_smul'ₓ'. -/
 theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateRow M j u) :=
@@ -710,7 +710,7 @@ theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) (SMul.smul.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (Matrix.hasSmul.{u1, u2, u2, u1} n n R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))))) s M) j u)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Fintype.card.{u2} n _inst_2) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u2, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s M) j u)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u1} n _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) (HSMul.hSMul.{u2, max u2 u1, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u2} n n R) (instHSMul.{u2, max u2 u1} R (Matrix.{u1, u1, u2} n n R) (Matrix.smul.{u2, u1, u1, u2} n n R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s M) j u)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Fintype.card.{u1} n _inst_2) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul' Matrix.det_updateColumn_smul'ₓ'. -/
 theorem det_updateColumn_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateColumn M j u) :=
@@ -731,7 +731,7 @@ Lemmas showing the determinant is invariant under a variety of operations.
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n n R} {B : Matrix.{u2, u2, u1} n n R} (C : Matrix.{u2, u2, u1} n n R), (Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 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_5))))))))) -> (Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) A (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_2 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) B C)) -> (Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 B))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R} {B : Matrix.{u1, u1, u2} n n R} (C : Matrix.{u1, u1, u2} n n R), (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 C) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) A (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_2 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) B C)) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 B))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R} {B : Matrix.{u1, u1, u2} n n R} (C : Matrix.{u1, u1, u2} n n R), (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 C) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) A (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_2 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) B C)) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 B))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_oneₓ'. -/
 theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = B ⬝ C) : det A = det B :=
@@ -746,7 +746,7 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n n R} {B : Matrix.{u2, u2, u1} n n R} (C : Matrix.{u2, u2, u1} n n R), (Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 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_5))))))))) -> (Eq.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n n R) A (Matrix.mul.{u1, u2, u2, u2} n n n R _inst_2 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) C B)) -> (Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 B))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R} {B : Matrix.{u1, u1, u2} n n R} (C : Matrix.{u1, u1, u2} n n R), (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 C) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) A (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_2 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) C B)) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 B))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n n R} {B : Matrix.{u1, u1, u2} n n R} (C : Matrix.{u1, u1, u2} n n R), (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 C) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))))) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u1, u1, u2} n n R) A (Matrix.mul.{u2, u1, u1, u1} n n n R _inst_2 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) C B)) -> (Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 B))
 Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mulₓ'. -/
 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = C ⬝ B) : det A = det B :=
@@ -786,7 +786,7 @@ theorem det_updateColumn_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n n R) {i : n} {j : 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_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) A 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_5))))) (A 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_5))))) c (A j))))) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R) {i : n} {j : 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_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) A 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_5)))))))) (A 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_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) c (A j))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R) {i : n} {j : 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_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) A 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_5)))))))) (A 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_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) c (A j))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_add_smul_self Matrix.det_updateRow_add_smul_selfₓ'. -/
 theorem det_updateRow_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateRow A i (A i + c • A j)) = det A := by
@@ -798,7 +798,7 @@ theorem det_updateRow_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j)
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n n R) {i : n} {j : 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_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) A i (fun (k : n) => HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (A k i) (SMul.smul.{u1, u1} R R (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) c (A k j))))) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R) {i : n} {j : 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_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) A i (fun (k : n) => HAdd.hAdd.{u2, u2, u2} R R R (instHAdd.{u2} R (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_5))))))) (A k i) (HSMul.hSMul.{u2, u2, u2} R R R (instHSMul.{u2, u2} R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) c (A k j))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R) {i : n} {j : 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_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) A i (fun (k : n) => HAdd.hAdd.{u2, u2, u2} R R R (instHAdd.{u2} R (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_5))))))) (A k i) (HSMul.hSMul.{u2, u2, u2} R R R (instHSMul.{u2, u2} R R (Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) c (A k j))))) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_add_smul_self Matrix.det_updateColumn_add_smul_selfₓ'. -/
 theorem det_updateColumn_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateColumn A i fun k => A k i + c • A k j) = det A :=
@@ -1195,7 +1195,7 @@ theorem det_succ_column {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (j :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R}, Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (fun (a : Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (b : Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) => Fin.decidableEq (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R _inst_5 A) (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_5))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R}, Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (a : Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (b : Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R _inst_5 A) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R}, Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (a : Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (b : Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R _inst_5 A) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)))))
 Case conversion may be inaccurate. Consider using '#align matrix.det_fin_zero Matrix.det_fin_zeroₓ'. -/
 /-- Determinant of 0x0 matrix -/
 @[simp]

86d1873c

bump to nightly-2023-05-03-22

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

aa7b8e08

Diff

@@ -675,7 +675,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5009 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5007 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_smul Matrix.det_updateRow_smulₓ'. -/
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
@@ -686,7 +686,7 @@ theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5081 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5079 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul Matrix.det_updateColumn_smulₓ'. -/
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=

86d1873c

bump to nightly-2023-04-27-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

c8f7a684

Diff

@@ -675,7 +675,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.4950 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5009 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateRow.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_smul Matrix.det_updateRow_smulₓ'. -/
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
@@ -686,7 +686,7 @@ theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
 lean 3 declaration is
   forall {n : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n] [_inst_2 : Fintype.{u2} n] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Matrix.{u2, u2, u1} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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_5))))) s u))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) s (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u1, u2, u2} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 but is expected to have type
-  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5021 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Matrix.{u1, u1, u2} n n R) (j : n) (s : R) (u : n -> R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j (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.LinearAlgebra.Matrix.Determinant._hyg.5081 : n) => R) (fun (i : n) => Algebra.toSMul.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5))))) s u))) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) s (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Matrix.updateColumn.{u2, u1, u1} n n R (fun (a : n) (b : n) => _inst_1 a b) M j u)))
 Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul Matrix.det_updateColumn_smulₓ'. -/
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=

86d1873c

bump to nightly-2023-04-25-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

56c36841

Diff

@@ -339,7 +339,7 @@ theorem det_mul_right_comm (M N P : Matrix m m R) : det (M ⬝ N ⬝ P) = det (M
 lean 3 declaration is
   forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (N : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) M) N) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Units.hasInv.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) M)))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 but is expected to have type
-  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInvUnits.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInv.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 Case conversion may be inaccurate. Consider using '#align matrix.det_units_conj Matrix.det_units_conjₓ'. -/
 theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M ⬝ N ⬝ ↑M⁻¹ : Matrix m m R) = det N := by
@@ -350,7 +350,7 @@ theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
 lean 3 declaration is
   forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (M : Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (N : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (Matrix.mul.{u1, u2, u2, u2} m m m R _inst_4 (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Units.hasInv.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) M)) N) ((fun (a : Type.{max u2 u1}) (b : Type.{max u2 u1}) [self : HasLiftT.{succ (max u2 u1), succ (max u2 u1)} a b] => self.0) (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (HasLiftT.mk.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (CoeTCₓ.coe.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (coeBase.{succ (max u2 u1), succ (max u2 u1)} (Units.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5)))) (Matrix.{u2, u2, u1} m m R) (Units.hasCoe.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Ring.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.ring.{u1, u2} m R _inst_4 (fun (a : m) (b : m) => _inst_3 a b) (CommRing.toRing.{u1} R _inst_5))))))) M))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 but is expected to have type
-  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInvUnits.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (M : Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (N : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Matrix.mul.{u2, u1, u1, u1} m m m R _inst_4 (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) (Inv.inv.{max u2 u1} (Units.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) (Units.instInv.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b))))) M)) N) (Units.val.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u1, u1, u2} m m R) (Matrix.semiring.{u2, u1} m R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)) _inst_4 (fun (a : m) (b : m) => _inst_3 a b)))) M))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 N)
 Case conversion may be inaccurate. Consider using '#align matrix.det_units_conj' Matrix.det_units_conj'ₓ'. -/
 theorem det_units_conj' (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M⁻¹ ⬝ N ⬝ ↑M : Matrix m m R) = det N :=

86d1873c

bump to nightly-2023-04-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

21a90077

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Chris Hughes, Tim Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.determinant
-! leanprover-community/mathlib commit c3019c79074b0619edb4b27553a91b2e82242395
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -22,6 +22,9 @@ import Mathbin.LinearAlgebra.Pi
 /-!
 # Determinant of a matrix
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the determinant of a matrix, `matrix.det`, and its essential properties.
 
 ## Main definitions

c3019c79

bump to nightly-2023-04-20-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

ffd433f8

Diff

@@ -59,25 +59,47 @@ variable {R : Type v} [CommRing R]
 -- mathport name: «exprε »
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
+#print Matrix.detRowAlternating /-
 /-- `det` is an `alternating_map` in the rows of the matrix. -/
 def detRowAlternating : AlternatingMap R (n → R) R n :=
   ((MultilinearMap.mkPiAlgebra R n R).compLinearMap LinearMap.proj).alternatization
 #align matrix.det_row_alternating Matrix.detRowAlternating
+-/
 
+#print Matrix.det /-
 /-- The determinant of a matrix given by the Leibniz formula. -/
 abbrev det (M : Matrix n n R) : R :=
   detRowAlternating M
 #align matrix.det Matrix.det
+-/
 
+/- warning: matrix.det_apply -> Matrix.det_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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 theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, σ.sign • ∏ i, M (σ i) i :=
   MultilinearMap.alternatization_apply _ M
 #align matrix.det_apply Matrix.det_apply
 
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 -- This is what the old definition was. We use it to avoid having to change the old proofs below
 theorem det_apply' (M : Matrix n n R) : M.det = ∑ σ : Perm n, ε σ * ∏ i, M (σ i) i := by
   simp [det_apply, Units.smul_def]
 #align matrix.det_apply' Matrix.det_apply'
 
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 @[simp]
 theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   by
@@ -94,18 +116,42 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
 
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 @[simp]
 theorem det_zero (h : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
 #align matrix.det_zero Matrix.det_zero
 
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 @[simp]
 theorem det_one : det (1 : Matrix n n R) = 1 := by rw [← diagonal_one] <;> simp [-diagonal_one]
 #align matrix.det_one Matrix.det_one
 
+/- warning: matrix.det_is_empty -> Matrix.det_isEmpty is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_is_empty Matrix.det_isEmptyₓ'. -/
 theorem det_isEmpty [IsEmpty n] {A : Matrix n n R} : det A = 1 := by simp [det_apply]
 #align matrix.det_is_empty Matrix.det_isEmpty
 
+/- warning: matrix.coe_det_is_empty -> Matrix.coe_det_isEmpty is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.coe_det_is_empty Matrix.coe_det_isEmptyₓ'. -/
 @[simp]
 theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.const _ 1 :=
   by
@@ -113,11 +159,23 @@ theorem coe_det_isEmpty [IsEmpty n] : (det : Matrix n n R → R) = Function.cons
   exact det_is_empty
 #align matrix.coe_det_is_empty Matrix.coe_det_isEmpty
 
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 theorem det_eq_one_of_card_eq_zero {A : Matrix n n R} (h : Fintype.card n = 0) : det A = 1 :=
   haveI : IsEmpty n := fintype.card_eq_zero_iff.mp h
   det_is_empty
 #align matrix.det_eq_one_of_card_eq_zero Matrix.det_eq_one_of_card_eq_zero
 
+/- warning: matrix.det_unique -> Matrix.det_unique is a dubious translation:
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 /-- If `n` has only one element, the determinant of an `n` by `n` matrix is just that element.
 Although `unique` implies `decidable_eq` and `fintype`, the instances might
 not be syntactically equal. Thus, we need to fill in the args explicitly. -/
@@ -126,18 +184,36 @@ theorem det_unique {n : Type _} [Unique n] [DecidableEq n] [Fintype n] (A : Matr
     det A = A default default := by simp [det_apply, univ_unique]
 #align matrix.det_unique Matrix.det_unique
 
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 theorem det_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) : det A = A k k :=
   by
   convert det_unique _
   exact uniqueOfSubsingleton k
 #align matrix.det_eq_elem_of_subsingleton Matrix.det_eq_elem_of_subsingleton
 
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 theorem det_eq_elem_of_card_eq_one {A : Matrix n n R} (h : Fintype.card n = 1) (k : n) :
     det A = A k k :=
   haveI : Subsingleton n := fintype.card_le_one_iff_subsingleton.mp h.le
   det_eq_elem_of_subsingleton _ _
 #align matrix.det_eq_elem_of_card_eq_one Matrix.det_eq_elem_of_card_eq_one
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_mul_aux Matrix.det_mul_auxₓ'. -/
 theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     (∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x) = 0 :=
   by
@@ -157,6 +233,12 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
       mul_swap_involutive i j σ
 #align matrix.det_mul_aux Matrix.det_mul_aux
 
+/- warning: matrix.det_mul -> Matrix.det_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_mul Matrix.det_mulₓ'. -/
 @[simp]
 theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
   calc
@@ -197,43 +279,87 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
     
 #align matrix.det_mul Matrix.det_mul
 
+#print Matrix.detMonoidHom /-
 /-- The determinant of a matrix, as a monoid homomorphism. -/
 def detMonoidHom : Matrix n n R →* R where
   toFun := det
   map_one' := det_one
   map_mul' := det_mul
 #align matrix.det_monoid_hom Matrix.detMonoidHom
+-/
 
+/- warning: matrix.coe_det_monoid_hom -> Matrix.coe_detMonoidHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHomₓ'. -/
 @[simp]
 theorem coe_detMonoidHom : (detMonoidHom : Matrix n n R → R) = det :=
   rfl
 #align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHom
 
+/- warning: matrix.det_mul_comm -> Matrix.det_mul_comm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_mul_comm Matrix.det_mul_commₓ'. -/
 /-- On square matrices, `mul_comm` applies under `det`. -/
 theorem det_mul_comm (M N : Matrix m m R) : det (M ⬝ N) = det (N ⬝ M) := by
   rw [det_mul, det_mul, mul_comm]
 #align matrix.det_mul_comm Matrix.det_mul_comm
 
+/- warning: matrix.det_mul_left_comm -> Matrix.det_mul_left_comm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_mul_left_comm Matrix.det_mul_left_commₓ'. -/
 /-- On square matrices, `mul_left_comm` applies under `det`. -/
 theorem det_mul_left_comm (M N P : Matrix m m R) : det (M ⬝ (N ⬝ P)) = det (N ⬝ (M ⬝ P)) := by
   rw [← Matrix.mul_assoc, ← Matrix.mul_assoc, det_mul, det_mul_comm M N, ← det_mul]
 #align matrix.det_mul_left_comm Matrix.det_mul_left_comm
 
+/- warning: matrix.det_mul_right_comm -> Matrix.det_mul_right_comm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_mul_right_comm Matrix.det_mul_right_commₓ'. -/
 /-- On square matrices, `mul_right_comm` applies under `det`. -/
 theorem det_mul_right_comm (M N P : Matrix m m R) : det (M ⬝ N ⬝ P) = det (M ⬝ P ⬝ N) := by
   rw [Matrix.mul_assoc, Matrix.mul_assoc, det_mul, det_mul_comm N P, ← det_mul]
 #align matrix.det_mul_right_comm Matrix.det_mul_right_comm
 
+/- warning: matrix.det_units_conj -> Matrix.det_units_conj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_units_conj Matrix.det_units_conjₓ'. -/
 theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M ⬝ N ⬝ ↑M⁻¹ : Matrix m m R) = det N := by
   rw [det_mul_right_comm, ← mul_eq_mul, ← mul_eq_mul, Units.mul_inv, one_mul]
 #align matrix.det_units_conj Matrix.det_units_conj
 
+/- warning: matrix.det_units_conj' -> Matrix.det_units_conj' is a dubious translation:
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 theorem det_units_conj' (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
     det (↑M⁻¹ ⬝ N ⬝ ↑M : Matrix m m R) = det N :=
   det_units_conj M⁻¹ N
 #align matrix.det_units_conj' Matrix.det_units_conj'
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_transpose Matrix.det_transposeₓ'. -/
 /-- Transposing a matrix preserves the determinant. -/
 @[simp]
 theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
@@ -248,12 +374,24 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det :=
   simp
 #align matrix.det_transpose Matrix.det_transpose
 
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 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = σ.sign * M.det :=
   ((detRowAlternating : AlternatingMap R (n → R) R n).map_perm M σ).trans (by simp [Units.smul_def])
 #align matrix.det_permute Matrix.det_permute
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_submatrix_equiv_self Matrix.det_submatrix_equiv_selfₓ'. -/
 /-- Permuting rows and columns with the same equivalence has no effect. -/
 @[simp]
 theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.submatrix e e) = det A :=
@@ -268,6 +406,12 @@ theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.subma
   rw [Equiv.permCongr_apply, Equiv.symm_apply_apply, submatrix_apply]
 #align matrix.det_submatrix_equiv_self Matrix.det_submatrix_equiv_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_reindex_self Matrix.det_reindex_selfₓ'. -/
 /-- Reindexing both indices along the same equivalence preserves the determinant.
 
 For the `simp` version of this lemma, see `det_submatrix_equiv_self`; this one is unsuitable because
@@ -277,6 +421,12 @@ theorem det_reindex_self (e : m ≃ n) (A : Matrix m m R) : det (reindex e e A)
   det_submatrix_equiv_self e.symm A
 #align matrix.det_reindex_self Matrix.det_reindex_self
 
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 /-- The determinant of a permutation matrix equals its sign. -/
 @[simp]
 theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matrix n n R) = σ.sign :=
@@ -285,6 +435,12 @@ theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matri
     det_permute, det_one, mul_one]
 #align matrix.det_permutation Matrix.det_permutation
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_smul Matrix.det_smulₓ'. -/
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
     det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
@@ -293,22 +449,46 @@ theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n
     
 #align matrix.det_smul Matrix.det_smul
 
+/- warning: matrix.det_smul_of_tower -> Matrix.det_smul_of_tower is a dubious translation:
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(Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7)))] [_inst_9 : SMulCommClass.{u3, u1, u1} α R R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7))) (Mul.toSMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5))))] (c : α) (A : Matrix.{u2, u2, u1} n n R), Eq.{succ u1} R (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (SMul.smul.{u3, max u2 u1} α (Matrix.{u2, u2, u1} n n R) (Matrix.hasSmul.{u1, u2, u2, u3} n n α R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7)))) c A)) (SMul.smul.{u3, u1} α R (SMulZeroClass.toHasSmul.{u3, u1} α R (AddZeroClass.toHasZero.{u1} R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (DistribSMul.toSmulZeroClass.{u3, u1} α R (AddMonoid.toAddZeroClass.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5)))))) (DistribMulAction.toDistribSMul.{u3, u1} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))) _inst_7))) (HPow.hPow.{u3, 0, u3} α Nat α (instHPow.{u3, 0} α Nat (Monoid.Pow.{u3} α _inst_6)) c (Fintype.card.{u2} n _inst_2)) (Matrix.det.{u1, u2} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+but is expected to have type
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u3}} [_inst_5 : CommRing.{u3} R] {α : Type.{u2}} [_inst_6 : Monoid.{u2} α] [_inst_7 : DistribMulAction.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))] [_inst_8 : IsScalarTower.{u2, u3, u3} α R R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))) (Algebra.toSMul.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_5) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_5)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7)))] [_inst_9 : SMulCommClass.{u2, u3, u3} α R R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))) (Algebra.toSMul.{u3, u3} R R (CommRing.toCommSemiring.{u3} R _inst_5) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_5)) (Algebra.id.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5)))] (c : α) (A : Matrix.{u1, u1, u3} n n R), Eq.{succ u3} R (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (HSMul.hSMul.{u2, max u3 u1, max u3 u1} α (Matrix.{u1, u1, u3} n n R) (Matrix.{u1, u1, u3} n n R) (instHSMul.{u2, max u3 u1} α (Matrix.{u1, u1, u3} n n R) (Matrix.smul.{u3, u1, u1, u2} n n α R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7))))) c A)) (HSMul.hSMul.{u2, u3, u3} α R R (instHSMul.{u2, u3} α R (SMulZeroClass.toSMul.{u2, u3} α R (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_5))) (DistribSMul.toSMulZeroClass.{u2, u3} α R (AddMonoid.toAddZeroClass.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5))))) (DistribMulAction.toDistribSMul.{u2, u3} α R _inst_6 (AddMonoidWithOne.toAddMonoid.{u3} R (AddGroupWithOne.toAddMonoidWithOne.{u3} R (Ring.toAddGroupWithOne.{u3} R (CommRing.toRing.{u3} R _inst_5)))) _inst_7)))) (HPow.hPow.{u2, 0, u2} α Nat α (instHPow.{u2, 0} α Nat (Monoid.Pow.{u2} α _inst_6)) c (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+Case conversion may be inaccurate. Consider using '#align matrix.det_smul_of_tower Matrix.det_smul_of_towerₓ'. -/
 @[simp]
 theorem det_smul_of_tower {α} [Monoid α] [DistribMulAction α R] [IsScalarTower α R R]
     [SMulCommClass α R R] (c : α) (A : Matrix n n R) : det (c • A) = c ^ Fintype.card n • det A :=
   by rw [← smul_one_smul R c A, det_smul, smul_pow, one_pow, smul_mul_assoc, one_mul]
 #align matrix.det_smul_of_tower Matrix.det_smul_of_tower
 
+/- warning: matrix.det_neg -> Matrix.det_neg is a dubious translation:
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+but is expected to have type
+  forall {n : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n] [_inst_2 : Fintype.{u1} n] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n n R), Eq.{succ u2} R (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 (Neg.neg.{max u2 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.neg.{u2, u1, u1} n n R (Ring.toNeg.{u2} R (CommRing.toRing.{u2} R _inst_5))) A)) (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))) (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Neg.neg.{u2} R (Ring.toNeg.{u2} R (CommRing.toRing.{u2} R _inst_5)) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Fintype.card.{u1} n _inst_2)) (Matrix.det.{u2, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 R _inst_5 A))
+Case conversion may be inaccurate. Consider using '#align matrix.det_neg Matrix.det_negₓ'. -/
 theorem det_neg (A : Matrix n n R) : det (-A) = (-1) ^ Fintype.card n * det A := by
   rw [← det_smul, neg_one_smul]
 #align matrix.det_neg Matrix.det_neg
 
+/- warning: matrix.det_neg_eq_smul -> Matrix.det_neg_eq_smul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.det_neg_eq_smul Matrix.det_neg_eq_smulₓ'. -/
 /-- A variant of `matrix.det_neg` with scalar multiplication by `units ℤ` instead of multiplication
 by `R`. -/
 theorem det_neg_eq_smul (A : Matrix n n R) : det (-A) = (-1 : Units ℤ) ^ Fintype.card n • det A :=
   by rw [← det_smul_of_tower, Units.neg_smul, one_smul]
 #align matrix.det_neg_eq_smul Matrix.det_neg_eq_smul
 
+/- warning: matrix.det_mul_row -> Matrix.det_mul_row is a dubious translation:
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 /-- Multiplying each row by a fixed `v i` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_row (v : n → R) (A : Matrix n n R) :
@@ -322,6 +502,12 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     
 #align matrix.det_mul_row Matrix.det_mul_row
 
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 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_column (v : n → R) (A : Matrix n n R) :
@@ -329,6 +515,12 @@ theorem det_mul_column (v : n → R) (A : Matrix n n R) :
   MultilinearMap.map_smul_univ _ v A
 #align matrix.det_mul_column Matrix.det_mul_column
 
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 @[simp]
 theorem det_pow (M : Matrix m m R) (n : ℕ) : det (M ^ n) = det M ^ n :=
   (detMonoidHom : Matrix m m R →* R).map_pow M n
@@ -338,19 +530,43 @@ section HomMap
 
 variable {S : Type w} [CommRing S]
 
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(Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (RingHom.instRingHomClassRingHom.{max u2 u1, max u3 u1} (Matrix.{u1, u1, u2} n n R) (Matrix.{u1, u1, u3} n n S) (Matrix.nonAssocSemiring.{u2, u1} n R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.nonAssocSemiring.{u3, u1} n S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (RingHom.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) f) M))
+Case conversion may be inaccurate. Consider using '#align ring_hom.map_det RingHom.map_detₓ'. -/
 theorem RingHom.map_det (f : R →+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
 #align ring_hom.map_det RingHom.map_det
 
+/- warning: ring_equiv.map_det -> RingEquiv.map_det is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5)))))) (Matrix.instMulMatrix.{u3, u1} n S _inst_2 (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (Matrix.add.{u2, u1, u1} n n R (Distrib.toAdd.{u2} R (NonUnitalNonAssocSemiring.toDistrib.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))))))) (Matrix.add.{u3, u1, u1} n n S (Distrib.toAdd.{u3} S (NonUnitalNonAssocSemiring.toDistrib.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6)))))))))))) (RingEquiv.mapMatrix.{u2, u3, u1} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_5))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_6))) f) M))
+Case conversion may be inaccurate. Consider using '#align ring_equiv.map_det RingEquiv.map_detₓ'. -/
 theorem RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align ring_equiv.map_det RingEquiv.map_det
 
+/- warning: alg_hom.map_det -> AlgHom.map_det is a dubious translation:
+lean 3 declaration is
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b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (Matrix.{u1, u1, u3} n n S) (fun (_x : Matrix.{u1, u1, u3} 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_inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (SMulZeroClass.toSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgHom.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) 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(CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)))))) (AlgHom.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+Case conversion may be inaccurate. Consider using '#align alg_hom.map_det AlgHom.map_detₓ'. -/
 theorem AlgHom.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S →ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toRingHom.map_det _
 #align alg_hom.map_det AlgHom.map_det
 
+/- warning: alg_equiv.map_det -> AlgEquiv.map_det is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CommRing.toRing.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))))) (AddCommMonoid.toAddMonoid.{u4} T (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)))) (Module.toDistribMulAction.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)) (Module.toDistribMulAction.{u2, u4} R T (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} T (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} T (Semiring.toNonAssocSemiring.{u4} T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8))))) (Algebra.toModule.{u2, u4} R T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u3, u4, max u3 u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) (AlgEquivClass.toAlgHomClass.{max u3 u4, u2, u3, u4} (AlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9) R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, u3, u4} R S T (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9)))))) f (Matrix.det.{u3, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 S _inst_6 M)) (Matrix.det.{u4, u1} n (fun (a : n) (b : n) => _inst_1 a b) _inst_2 T _inst_8 (FunLike.coe.{max (max (succ u3) (succ u4)) (succ u1), max (succ u3) (succ u1), max (succ u4) (succ u1)} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) 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(CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (SMulZeroClass.toSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toZero.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (AddMonoid.toAddZeroClass.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribMulAction.toDistribSMul.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, 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(CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7)))))) (SMulZeroClass.toSMul.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (AddMonoid.toZero.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))))) (DistribSMul.toSMulZeroClass.{u2, max u4 u1} 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(Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) 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_inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (AddCommMonoid.toAddMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (AddCommMonoid.toAddMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) 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(Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max u3 u4) u1, u2, max u3 u1, max u4 u1} (AlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)))) (Module.toDistribMulAction.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Semiring.toNonAssocSemiring.{max u3 u1} (Matrix.{u1, u1, u3} n n S) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u3 u1} R (Matrix.{u1, u1, u3} n n S) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7))) (Module.toDistribMulAction.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_5)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Semiring.toNonAssocSemiring.{max u4 u1} (Matrix.{u1, u1, u4} n n T) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b))))) (Algebra.toModule.{u2, max u4 u1} R (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, max u3 u1, max u4 u1, max (max u3 u4) u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) 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(Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9)) R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9) (AlgEquiv.instAlgEquivClassAlgEquiv.{u2, max u3 u1, max u4 u1} R (Matrix.{u1, u1, u3} n n S) (Matrix.{u1, u1, u4} n n T) (CommRing.toCommSemiring.{u2} R _inst_5) (Matrix.semiring.{u3, u1} n S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.semiring.{u4, u1} n T (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_2 (fun (a : n) (b : n) => _inst_1 a b)) (Matrix.instAlgebraMatrixSemiring.{u3, u1, u2} n R S _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) _inst_7) (Matrix.instAlgebraMatrixSemiring.{u4, u1, u2} n R T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_9))))))) (AlgEquiv.mapMatrix.{u3, u4, u1, u2} n R S T _inst_2 (fun (a : n) (b : n) => _inst_1 a b) (CommRing.toCommSemiring.{u2} R _inst_5) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_6)) (Ring.toSemiring.{u4} T (CommRing.toRing.{u4} T _inst_8)) _inst_7 _inst_9 f) M))
+Case conversion may be inaccurate. Consider using '#align alg_equiv.map_det AlgEquiv.map_detₓ'. -/
 theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (f : S ≃ₐ[R] T)
     (M : Matrix n n S) : f M.det = Matrix.det (f.mapMatrix M) :=
   f.toAlgHom.map_det _
@@ -358,6 +574,12 @@ theorem AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra R T] (
 
 end HomMap
 
+/- warning: matrix.det_conj_transpose -> Matrix.det_conjTranspose is a dubious translation:
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+  forall {m : Type.{u2}} [_inst_3 : DecidableEq.{succ u2} m] [_inst_4 : Fintype.{u2} m] {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5)))] (M : Matrix.{u2, u2, u1} m m R), Eq.{succ u1} R (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.conjTranspose.{u1, u2, u2} m m R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5))) _inst_6))) M)) (Star.star.{u1} R (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_5))) _inst_6))) (Matrix.det.{u1, u2} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M))
+but is expected to have type
+  forall {m : Type.{u1}} [_inst_3 : DecidableEq.{succ u1} m] [_inst_4 : Fintype.{u1} m] {R : Type.{u2}} [_inst_5 : CommRing.{u2} R] [_inst_6 : StarRing.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5)))] (M : Matrix.{u1, u1, u2} m m R), Eq.{succ u2} R (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 (Matrix.conjTranspose.{u2, u1, u1} m m R (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5))) _inst_6))) M)) (Star.star.{u2} R (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (Ring.toAddGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_5)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_5))) _inst_6))) (Matrix.det.{u2, u1} m (fun (a : m) (b : m) => _inst_3 a b) _inst_4 R _inst_5 M))
+Case conversion may be inaccurate. Consider using '#align matrix.det_conj_transpose Matrix.det_conjTransposeₓ'. -/
 @[simp]
 theorem det_conjTranspose [StarRing R] (M : Matrix m m R) : det Mᴴ = star (det M) :=
   ((starRingEnd R).map_det _).symm.trans <| congr_arg star M.det_transpose
@@ -372,10 +594,22 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 -/
 
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zeroₓ'. -/
 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_zero_of_column_eq_zero Matrix.det_eq_zero_of_column_eq_zeroₓ'. -/
 theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) : det A = 0 :=
   by
   rw [← det_transpose]
@@ -384,11 +618,23 @@ theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i
 
 variable {M : Matrix n n R} {i j : n}
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_zero_of_row_eq Matrix.det_zero_of_row_eqₓ'. -/
 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_eq_zero_of_eq M hij i_ne_j
 #align matrix.det_zero_of_row_eq Matrix.det_zero_of_row_eq
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_zero_of_column_eq Matrix.det_zero_of_column_eqₓ'. -/
 /-- If a matrix has a repeated column, the determinant will be zero. -/
 theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) : M.det = 0 :=
   by
@@ -398,11 +644,23 @@ theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) :
 
 end DetZero
 
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 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_add M j u v
 #align matrix.det_update_row_add Matrix.det_updateRow_add
 
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 theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateColumn M j <| u + v) = det (updateColumn M j u) + det (updateColumn M j v) :=
   by
@@ -410,11 +668,23 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_add Matrix.det_updateColumn_add
 
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 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_smul M j s u
 #align matrix.det_update_row_smul Matrix.det_updateRow_smul
 
+/- warning: matrix.det_update_column_smul -> Matrix.det_updateColumn_smul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul Matrix.det_updateColumn_smulₓ'. -/
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn M j <| s • u) = s * det (updateColumn M j u) :=
   by
@@ -422,11 +692,23 @@ theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
   simp [update_row_transpose, det_transpose]
 #align matrix.det_update_column_smul Matrix.det_updateColumn_smul
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_smul' Matrix.det_updateRow_smul'ₓ'. -/
 theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateRow M j u) :=
   MultilinearMap.map_update_smul _ M j s u
 #align matrix.det_update_row_smul' Matrix.det_updateRow_smul'
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_smul' Matrix.det_updateColumn_smul'ₓ'. -/
 theorem det_updateColumn_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateColumn (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateColumn M j u) :=
   by
@@ -442,6 +724,12 @@ Lemmas showing the determinant is invariant under a variety of operations.
 -/
 
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_oneₓ'. -/
 theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = B ⬝ C) : det A = det B :=
   calc
@@ -451,6 +739,12 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mulₓ'. -/
 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
     (hA : A = C ⬝ B) : det A = det B :=
   calc
@@ -460,12 +754,24 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_add_self Matrix.det_updateRow_add_selfₓ'. -/
 theorem det_updateRow_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
     det (updateRow A i (A i + A j)) = det A := by
   simp [det_update_row_add,
     det_zero_of_row_eq hij (update_row_self.trans (update_row_ne hij.symm).symm)]
 #align matrix.det_update_row_add_self Matrix.det_updateRow_add_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_add_self Matrix.det_updateColumn_add_selfₓ'. -/
 theorem det_updateColumn_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
     det (updateColumn A i fun k => A k i + A k j) = det A :=
   by
@@ -473,12 +779,24 @@ theorem det_updateColumn_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :
   exact det_update_row_add_self Aᵀ hij
 #align matrix.det_update_column_add_self Matrix.det_updateColumn_add_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_row_add_smul_self Matrix.det_updateRow_add_smul_selfₓ'. -/
 theorem det_updateRow_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateRow A i (A i + c • A j)) = det A := by
   simp [det_update_row_add, det_update_row_smul,
     det_zero_of_row_eq hij (update_row_self.trans (update_row_ne hij.symm).symm)]
 #align matrix.det_update_row_add_smul_self Matrix.det_updateRow_add_smul_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_update_column_add_smul_self Matrix.det_updateColumn_add_smul_selfₓ'. -/
 theorem det_updateColumn_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) (c : R) :
     det (updateColumn A i fun k => A k i + c • A k j) = det A :=
   by
@@ -486,6 +804,12 @@ theorem det_updateColumn_add_smul_self (A : Matrix n n R) {i j : n} (hij : i ≠
   exact det_update_row_add_smul_self Aᵀ hij c
 #align matrix.det_update_column_add_smul_self Matrix.det_updateColumn_add_smul_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_const_aux Matrix.det_eq_of_forall_row_eq_smul_add_const_auxₓ'. -/
 theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Finset n} :
     ∀ (c : n → R) (hs : ∀ i, i ∉ s → c i = 0) (k : n) (hk : k ∉ s)
       (A_eq : ∀ i j, A i j = B i j + c i * B k j), det A = det B :=
@@ -518,6 +842,12 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       rw [A_eq, update_row_ne fun h : k = i => hk <| h ▸ Finset.mem_insert_self k s]
 #align matrix.det_eq_of_forall_row_eq_smul_add_const_aux Matrix.det_eq_of_forall_row_eq_smul_add_const_aux
 
+/- warning: matrix.det_eq_of_forall_row_eq_smul_add_const -> Matrix.det_eq_of_forall_row_eq_smul_add_const is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_const Matrix.det_eq_of_forall_row_eq_smul_add_constₓ'. -/
 /-- If you add multiples of row `B k` to other rows, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R) (k : n)
     (hk : c k = 0) (A_eq : ∀ i j, A i j = B i j + c i * B k j) : det A = det B :=
@@ -529,6 +859,12 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
     k (Finset.not_mem_erase k Finset.univ) A_eq
 #align matrix.det_eq_of_forall_row_eq_smul_add_const Matrix.det_eq_of_forall_row_eq_smul_add_const
 
+/- warning: matrix.det_eq_of_forall_row_eq_smul_add_pred_aux -> Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_auxₓ'. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (hc : ∀ i : Fin n, k < i.succ → c i = 0)
       {M N : Matrix (Fin n.succ) (Fin n.succ) R} (h0 : ∀ j, M 0 j = N 0 j)
@@ -568,6 +904,12 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ j, A 0 j = B 0 j)
@@ -576,6 +918,12 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
     (fun i hi => absurd hi (not_lt_of_ge (Fin.le_last _))) A_zero A_succ
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred Matrix.det_eq_of_forall_row_eq_smul_add_pred
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_eq_of_forall_col_eq_smul_add_pred Matrix.det_eq_of_forall_col_eq_smul_add_predₓ'. -/
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ i, A i 0 = B i 0)
@@ -587,6 +935,12 @@ theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 
 end DetEq
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_block_diagonal Matrix.det_blockDiagonalₓ'. -/
 @[simp]
 theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Matrix n n R) :
     (blockDiagonal M).det = ∏ k, (M k).det :=
@@ -662,6 +1016,12 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
     exact hkx
 #align matrix.det_block_diagonal Matrix.det_blockDiagonal
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁ₓ'. -/
 /-- The determinant of a 2×2 block matrix with the lower-left block equal to zero is the product of
 the determinants of the diagonal blocks. For the generalization to any number of blocks, see
 `matrix.det_of_upper_triangular`. -/
@@ -723,6 +1083,12 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
         rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁
 
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+Case conversion may be inaccurate. Consider using '#align matrix.det_from_blocks_zero₁₂ Matrix.det_fromBlocks_zero₁₂ₓ'. -/
 /-- The determinant of a 2×2 block matrix with the upper-right block equal to zero is the product of
 the determinants of the diagonal blocks. For the generalization to any number of blocks, see
 `matrix.det_of_lower_triangular`. -/
@@ -733,6 +1099,7 @@ theorem det_fromBlocks_zero₁₂ (A : Matrix m m R) (C : Matrix n m R) (D : Mat
     det_transpose]
 #align matrix.det_from_blocks_zero₁₂ Matrix.det_fromBlocks_zero₁₂
 
+#print Matrix.det_succ_column_zero /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along column 0. -/
 theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) :
     det A = ∑ i : Fin n.succ, (-1) ^ (i : ℕ) * A i 0 * det (A.submatrix i.succAbove Fin.succ) :=
@@ -771,7 +1138,9 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
         Fin.succAbove_cycleRange]
     
 #align matrix.det_succ_column_zero Matrix.det_succ_column_zero
+-/
 
+#print Matrix.det_succ_row_zero /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along row 0. -/
 theorem det_succ_row_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) :
     det A = ∑ j : Fin n.succ, (-1) ^ (j : ℕ) * A 0 j * det (A.submatrix Fin.succ j.succAbove) :=
@@ -781,7 +1150,9 @@ theorem det_succ_row_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) :
   rw [← det_transpose]
   simp only [transpose_apply, transpose_submatrix, transpose_transpose]
 #align matrix.det_succ_row_zero Matrix.det_succ_row_zero
+-/
 
+#print Matrix.det_succ_row /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along row `i`. -/
 theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin n.succ) :
     det A =
@@ -803,7 +1174,9 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
   · ext (i' j')
     rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_succ]
 #align matrix.det_succ_row Matrix.det_succ_row
+-/
 
+#print Matrix.det_succ_column /-
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along column `j`. -/
 theorem det_succ_column {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (j : Fin n.succ) :
     det A =
@@ -813,22 +1186,43 @@ theorem det_succ_column {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (j :
   refine' Finset.sum_congr rfl fun i _ => _
   rw [add_comm, ← det_transpose, transpose_apply, transpose_submatrix, transpose_transpose]
 #align matrix.det_succ_column Matrix.det_succ_column
+-/
 
+/- warning: matrix.det_fin_zero -> Matrix.det_fin_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R}, Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (fun (a : Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (b : Fin (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) => Fin.decidableEq (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) R _inst_5 A) (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_5))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] {A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R}, Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (a : Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (b : Fin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) R _inst_5 A) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5)))))
+Case conversion may be inaccurate. Consider using '#align matrix.det_fin_zero Matrix.det_fin_zeroₓ'. -/
 /-- Determinant of 0x0 matrix -/
 @[simp]
 theorem det_fin_zero {A : Matrix (Fin 0) (Fin 0) R} : det A = 1 :=
   det_isEmpty
 #align matrix.det_fin_zero Matrix.det_fin_zero
 
+/- warning: matrix.det_fin_one -> Matrix.det_fin_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) R), Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (fun (a : Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (b : Fin (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) => Fin.decidableEq (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) R _inst_5 A) (A (OfNat.ofNat.{0} (Fin (One.one.{0} Nat Nat.hasOne)) 0 (OfNat.mk.{0} (Fin (One.one.{0} Nat Nat.hasOne)) 0 (Zero.zero.{0} (Fin (One.one.{0} Nat Nat.hasOne)) (Fin.hasZeroOfNeZero (One.one.{0} Nat Nat.hasOne) (NeZero.one.{0} Nat (NonAssocSemiring.toMulZeroOneClass.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) Nat.nontrivial))))) (OfNat.ofNat.{0} (Fin (One.one.{0} Nat Nat.hasOne)) 0 (OfNat.mk.{0} (Fin (One.one.{0} Nat Nat.hasOne)) 0 (Zero.zero.{0} (Fin (One.one.{0} Nat Nat.hasOne)) (Fin.hasZeroOfNeZero (One.one.{0} Nat Nat.hasOne) (NeZero.one.{0} Nat (NonAssocSemiring.toMulZeroOneClass.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring)) Nat.nontrivial))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) R), Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (fun (a : Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (b : Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) R _inst_5 A) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align matrix.det_fin_one Matrix.det_fin_oneₓ'. -/
 /-- Determinant of 1x1 matrix -/
 theorem det_fin_one (A : Matrix (Fin 1) (Fin 1) R) : det A = A 0 0 :=
   det_unique A
 #align matrix.det_fin_one Matrix.det_fin_one
 
+#print Matrix.det_fin_one_of /-
 theorem det_fin_one_of (a : R) : det !![a] = a :=
   det_fin_one _
 #align matrix.det_fin_one_of Matrix.det_fin_one_of
+-/
 
+/- warning: matrix.det_fin_two -> Matrix.det_fin_two is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R), Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (b : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => Fin.decidableEq (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) R _inst_5 A) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddGroupWithOne.toAddGroup.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_5))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (A (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))) (A (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_5)))) (A (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring))))))) (A (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 1 (One.one.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasOneOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))) (OfNat.ofNat.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (OfNat.mk.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) 0 (Zero.zero.{0} (Fin (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))) (Fin.hasZeroOfNeZero (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)) (CharZero.NeZero.two.{0} Nat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} Nat (NonAssocSemiring.toAddCommMonoidWithOne.{0} Nat (Semiring.toNonAssocSemiring.{0} Nat Nat.semiring))) (StrictOrderedSemiring.to_charZero.{0} Nat Nat.strictOrderedSemiring)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] (A : Matrix.{0, 0, u1} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) R), Eq.{succ u1} R (Matrix.det.{u1, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (b : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => instDecidableEqFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) a b) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) R _inst_5 A) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (Ring.toSub.{u1} R (CommRing.toRing.{u1} R _inst_5))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_5))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (A (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 1 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 1 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (OfNat.ofNat.{0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) 0 (Fin.instOfNatFin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) 0 (NeZero.succ (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))
+Case conversion may be inaccurate. Consider using '#align matrix.det_fin_two Matrix.det_fin_twoₓ'. -/
 /-- Determinant of 2x2 matrix -/
 theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0 1 * A 1 0 :=
   by
@@ -836,11 +1230,14 @@ theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0
   ring
 #align matrix.det_fin_two Matrix.det_fin_two
 
+#print Matrix.det_fin_two_of /-
 @[simp]
 theorem det_fin_two_of (a b c d : R) : Matrix.det !![a, b; c, d] = a * d - b * c :=
   det_fin_two _
 #align matrix.det_fin_two_of Matrix.det_fin_two_of
+-/
 
+#print Matrix.det_fin_three /-
 /-- Determinant of 3x3 matrix -/
 theorem det_fin_three (A : Matrix (Fin 3) (Fin 3) R) :
     det A =
@@ -852,6 +1249,7 @@ theorem det_fin_three (A : Matrix (Fin 3) (Fin 3) R) :
   simp [Matrix.det_succ_row_zero, Fin.sum_univ_succ]
   ring
 #align matrix.det_fin_three Matrix.det_fin_three
+-/
 
 end Matrix

c3019c79

bump to nightly-2023-04-20-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

fbfe5c3e

Diff

@@ -652,7 +652,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
       simp only [mk_inv_apply_eq, apply_inv_self]
     · apply Finset.mem_univ
     · ext ⟨k, x⟩
-      · simp only [[anonymous], prod_congr_left_apply]
+      · simp only [coe_fn_mk, prod_congr_left_apply]
       · simp only [prod_congr_left_apply, hσ]
   · intro σ _ hσ
     rw [mem_preserving_snd] at hσ

c3019c79

bump to nightly-2023-04-18-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

7809aa1d

Diff

@@ -825,7 +825,6 @@ theorem det_fin_one (A : Matrix (Fin 1) (Fin 1) R) : det A = A 0 0 :=
   det_unique A
 #align matrix.det_fin_one Matrix.det_fin_one
 
-/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
 theorem det_fin_one_of (a : R) : det !![a] = a :=
   det_fin_one _
 #align matrix.det_fin_one_of Matrix.det_fin_one_of
@@ -837,7 +836,6 @@ theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0
   ring
 #align matrix.det_fin_two Matrix.det_fin_two
 
-/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
 @[simp]
 theorem det_fin_two_of (a b c d : R) : Matrix.det !![a, b; c, d] = a * d - b * c :=
   det_fin_two _

c3019c79

bump to nightly-2023-04-17-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

ce473067

Diff

@@ -825,13 +825,8 @@ theorem det_fin_one (A : Matrix (Fin 1) (Fin 1) R) : det A = A 0 0 :=
   det_unique A
 #align matrix.det_fin_one Matrix.det_fin_one
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
-theorem det_fin_one_of (a : R) :
-    det
-        («expr!![ »
-          "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation") =
-      a :=
+/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
+theorem det_fin_one_of (a : R) : det !![a] = a :=
   det_fin_one _
 #align matrix.det_fin_one_of Matrix.det_fin_one_of
 
@@ -842,14 +837,9 @@ theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0
   ring
 #align matrix.det_fin_two Matrix.det_fin_two
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
 @[simp]
-theorem det_fin_two_of (a b c d : R) :
-    Matrix.det
-        («expr!![ »
-          "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation") =
-      a * d - b * c :=
+theorem det_fin_two_of (a b c d : R) : Matrix.det !![a, b; c, d] = a * d - b * c :=
   det_fin_two _
 #align matrix.det_fin_two_of Matrix.det_fin_two_of

c3019c79

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -670,8 +670,8 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     (Matrix.fromBlocks A B 0 D).det = A.det * D.det := by
   classical
     simp_rw [det_apply']
-    convert
-      (sum_subset (subset_univ ((sum_congr_hom m n).range : Set (perm (Sum m n))).toFinset) _).symm
+    convert(sum_subset (subset_univ ((sum_congr_hom m n).range : Set (perm (Sum m n))).toFinset)
+          _).symm
     rw [sum_mul_sum]
     simp_rw [univ_product_univ]
     rw [(sum_bij (fun (σ : perm m × perm n) _ => Equiv.sumCongr σ.fst σ.snd) _ _ _ _).symm]

c3019c79

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -85,7 +85,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i :=
   refine' (Finset.sum_eq_single 1 _ _).trans _
   · intro σ h1 h2
     cases' not_forall.1 (mt Equiv.ext h2) with x h3
-    convert mul_zero _
+    convert MulZeroClass.mul_zero _
     apply Finset.prod_eq_zero
     · change x ∈ _
       simp
@@ -500,7 +500,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       simp [hs]
     congr
     ext (i j)
-    rw [A_eq, this, zero_mul, add_zero]
+    rw [A_eq, this, MulZeroClass.zero_mul, add_zero]
   · intro i s hi ih B c hs k hk A_eq
     have hAi : A i = B i + c i • B k := funext (A_eq i)
     rw [@ih (update_row B i (A i)) (Function.update c i 0), hAi, det_update_row_add_smul_self]
@@ -538,7 +538,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · congr
     ext (i j)
     refine' Fin.cases (h0 j) (fun i => _) i
-    rw [hsucc, hc i (Fin.succ_pos _), zero_mul, add_zero]
+    rw [hsucc, hc i (Fin.succ_pos _), MulZeroClass.zero_mul, add_zero]
   set M' := update_row M k.succ (N k.succ) with hM'
   have hM : M = update_row M' k.succ (M' k.succ + c k • M k.cast_succ) :=
     by
@@ -559,7 +559,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   intro i j
   rw [Function.update_apply]
   split_ifs with hik
-  · rw [zero_mul, add_zero, hM', hik, update_row_self]
+  · rw [MulZeroClass.zero_mul, add_zero, hM', hik, update_row_self]
   rw [hM', update_row_ne ((Fin.succ_injective _).Ne hik), hsucc]
   by_cases hik2 : k < i
   · simp [hc i (fin.succ_lt_succ_iff.mpr hik2)]
@@ -657,7 +657,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
   · intro σ _ hσ
     rw [mem_preserving_snd] at hσ
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
-    rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), mul_zero]
+    rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), MulZeroClass.mul_zero]
     rw [← @Prod.mk.eta _ _ (σ (k, x)), block_diagonal_apply_ne]
     exact hkx
 #align matrix.det_block_diagonal Matrix.det_blockDiagonal
@@ -718,7 +718,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       cases' hx : σ (Sum.inl a) with a2 b
       · have hn := (not_exists.mp ha) a2
         exact absurd hx.symm hn
-      · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), mul_zero]
+      · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
         rw [hx, from_blocks_apply₂₁]
         rfl
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁

c3019c79

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -166,17 +166,17 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
     _ =
         ∑ p in (@univ (n → n) _).filterₓ Bijective,
           ∑ σ : Perm n, ε σ * ∏ i, M (σ i) (p i) * N (p i) i :=
-      Eq.symm <|
+      (Eq.symm <|
         sum_subset (filter_subset _ _) fun f _ hbij =>
-          det_mul_aux <| by simpa only [true_and_iff, mem_filter, mem_univ] using hbij
+          det_mul_aux <| by simpa only [true_and_iff, mem_filter, mem_univ] using hbij)
     _ = ∑ τ : Perm n, ∑ σ : Perm n, ε σ * ∏ i, M (σ i) (τ i) * N (τ i) i :=
-      sum_bij (fun p h => Equiv.ofBijective p (mem_filter.1 h).2) (fun _ _ => mem_univ _)
+      (sum_bij (fun p h => Equiv.ofBijective p (mem_filter.1 h).2) (fun _ _ => mem_univ _)
         (fun _ _ => rfl) (fun _ _ _ _ h => by injection h) fun b _ =>
-        ⟨b, mem_filter.2 ⟨mem_univ _, b.Bijective⟩, coe_fn_injective rfl⟩
+        ⟨b, mem_filter.2 ⟨mem_univ _, b.Bijective⟩, coe_fn_injective rfl⟩)
     _ = ∑ σ : Perm n, ∑ τ : Perm n, (∏ i, N (σ i) i) * ε τ * ∏ j, M (τ j) (σ j) := by
       simp only [mul_comm, mul_left_comm, prod_mul_distrib, mul_assoc]
     _ = ∑ σ : Perm n, ∑ τ : Perm n, (∏ i, N (σ i) i) * (ε σ * ε τ) * ∏ i, M (τ i) i :=
-      sum_congr rfl fun σ _ =>
+      (sum_congr rfl fun σ _ =>
         Fintype.sum_equiv (Equiv.mulRight σ⁻¹) _ _ fun τ =>
           by
           have : (∏ j, M (τ j) (σ j)) = ∏ j, M ((τ * σ⁻¹) j) j :=
@@ -192,7 +192,7 @@ theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
               _ = ε τ := by simp only [inv_mul_cancel_right]
               
           simp_rw [Equiv.coe_mulRight, h]
-          simp only [this]
+          simp only [this])
     _ = det M * det N := by simp only [det_apply', Finset.mul_sum, mul_comm, mul_left_comm]
     
 #align matrix.det_mul Matrix.det_mul
@@ -288,7 +288,7 @@ theorem det_permutation (σ : Perm n) : Matrix.det (σ.toPEquiv.toMatrix : Matri
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
     det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
-    _ = det (diagonal fun _ => c) * det A := det_mul _ _
+    _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
     
 #align matrix.det_smul Matrix.det_smul
@@ -446,7 +446,7 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     (hA : A = B ⬝ C) : det A = det B :=
   calc
     det A = det (B ⬝ C) := congr_arg _ hA
-    _ = det B * det C := det_mul _ _
+    _ = det B * det C := (det_mul _ _)
     _ = det B := by rw [hC, mul_one]
     
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
@@ -455,7 +455,7 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     (hA : A = C ⬝ B) : det A = det B :=
   calc
     det A = det (C ⬝ B) := congr_arg _ hA
-    _ = det C * det B := det_mul _ _
+    _ = det C * det B := (det_mul _ _)
     _ = det B := by rw [hC, one_mul]
     
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul
@@ -826,11 +826,11 @@ theorem det_fin_one (A : Matrix (Fin 1) (Fin 1) R) : det A = A 0 0 :=
 #align matrix.det_fin_one Matrix.det_fin_one
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 theorem det_fin_one_of (a : R) :
     det
         («expr!![ »
-          "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation") =
+          "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation") =
       a :=
   det_fin_one _
 #align matrix.det_fin_one_of Matrix.det_fin_one_of
@@ -843,12 +843,12 @@ theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0
 #align matrix.det_fin_two Matrix.det_fin_two
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
 @[simp]
 theorem det_fin_two_of (a b c d : R) :
     Matrix.det
         («expr!![ »
-          "./././Mathport/Syntax/Translate/Expr.lean:391:14: unsupported user notation matrix.notation") =
+          "./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation") =
       a * d - b * c :=
   det_fin_two _
 #align matrix.det_fin_two_of Matrix.det_fin_two_of

c3019c79

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

c3019c79

chore: adapt to multiple goal linter 3 (#12372)

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

d29b3780

Diff

@@ -589,50 +589,50 @@ theorem det_blockDiagonal {o : Type*} [Fintype o] [DecidableEq o] (M : o → Mat
     Finset.mem_filter.trans ⟨fun h => h.2, fun h => ⟨Finset.mem_univ _, h⟩⟩
   rw [← Finset.sum_subset (Finset.subset_univ preserving_snd) _]
   -- And that these are in bijection with `o → Equiv.Perm m`.
-  refine (Finset.sum_bij (fun σ _ => prodCongrLeft fun k ↦ σ k (mem_univ k)) ?_ ?_ ?_ ?_).symm
-  · intro σ _
-    rw [mem_preserving_snd]
-    rintro ⟨-, x⟩
-    simp only [prodCongrLeft_apply]
-  · intro σ _ σ' _ eq
-    ext x hx k
-    simp only at eq
-    have :
-      ∀ k x,
-        prodCongrLeft (fun k => σ k (Finset.mem_univ _)) (k, x) =
-          prodCongrLeft (fun k => σ' k (Finset.mem_univ _)) (k, x) :=
-      fun k x => by rw [eq]
-    simp only [prodCongrLeft_apply, Prod.mk.inj_iff] at this
-    exact (this k x).1
-  · intro σ hσ
-    rw [mem_preserving_snd] at hσ
-    have hσ' : ∀ x, (σ⁻¹ x).snd = x.snd := by
-      intro x
-      conv_rhs => rw [← Perm.apply_inv_self σ x, hσ]
-    have mk_apply_eq : ∀ k x, ((σ (x, k)).fst, k) = σ (x, k) := by
-      intro k x
-      ext
-      · simp only
-      · simp only [hσ]
-    have mk_inv_apply_eq : ∀ k x, ((σ⁻¹ (x, k)).fst, k) = σ⁻¹ (x, k) := by
-      intro k x
-      conv_lhs => rw [← Perm.apply_inv_self σ (x, k)]
-      ext
-      · simp only [apply_inv_self]
-      · simp only [hσ']
-    refine' ⟨fun k _ => ⟨fun x => (σ (x, k)).fst, fun x => (σ⁻¹ (x, k)).fst, _, _⟩, _, _⟩
-    · intro x
-      simp only [mk_apply_eq, inv_apply_self]
-    · intro x
-      simp only [mk_inv_apply_eq, apply_inv_self]
-    · apply Finset.mem_univ
-    · ext ⟨k, x⟩
-      · simp only [coe_fn_mk, prodCongrLeft_apply]
-      · simp only [prodCongrLeft_apply, hσ]
-  · intro σ _
-    rw [Finset.prod_mul_distrib, ← Finset.univ_product_univ, Finset.prod_product_right]
-    simp only [sign_prodCongrLeft, Units.coe_prod, Int.cast_prod, blockDiagonal_apply_eq,
-      prodCongrLeft_apply]
+  · refine (Finset.sum_bij (fun σ _ => prodCongrLeft fun k ↦ σ k (mem_univ k)) ?_ ?_ ?_ ?_).symm
+    · intro σ _
+      rw [mem_preserving_snd]
+      rintro ⟨-, x⟩
+      simp only [prodCongrLeft_apply]
+    · intro σ _ σ' _ eq
+      ext x hx k
+      simp only at eq
+      have :
+        ∀ k x,
+          prodCongrLeft (fun k => σ k (Finset.mem_univ _)) (k, x) =
+            prodCongrLeft (fun k => σ' k (Finset.mem_univ _)) (k, x) :=
+        fun k x => by rw [eq]
+      simp only [prodCongrLeft_apply, Prod.mk.inj_iff] at this
+      exact (this k x).1
+    · intro σ hσ
+      rw [mem_preserving_snd] at hσ
+      have hσ' : ∀ x, (σ⁻¹ x).snd = x.snd := by
+        intro x
+        conv_rhs => rw [← Perm.apply_inv_self σ x, hσ]
+      have mk_apply_eq : ∀ k x, ((σ (x, k)).fst, k) = σ (x, k) := by
+        intro k x
+        ext
+        · simp only
+        · simp only [hσ]
+      have mk_inv_apply_eq : ∀ k x, ((σ⁻¹ (x, k)).fst, k) = σ⁻¹ (x, k) := by
+        intro k x
+        conv_lhs => rw [← Perm.apply_inv_self σ (x, k)]
+        ext
+        · simp only [apply_inv_self]
+        · simp only [hσ']
+      refine' ⟨fun k _ => ⟨fun x => (σ (x, k)).fst, fun x => (σ⁻¹ (x, k)).fst, _, _⟩, _, _⟩
+      · intro x
+        simp only [mk_apply_eq, inv_apply_self]
+      · intro x
+        simp only [mk_inv_apply_eq, apply_inv_self]
+      · apply Finset.mem_univ
+      · ext ⟨k, x⟩
+        · simp only [coe_fn_mk, prodCongrLeft_apply]
+        · simp only [prodCongrLeft_apply, hσ]
+    · intro σ _
+      rw [Finset.prod_mul_distrib, ← Finset.univ_product_univ, Finset.prod_product_right]
+      simp only [sign_prodCongrLeft, Units.coe_prod, Int.cast_prod, blockDiagonal_apply_eq,
+        prodCongrLeft_apply]
   · intro σ _ hσ
     rw [mem_preserving_snd] at hσ
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
@@ -651,37 +651,37 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     simp_rw [det_apply']
     convert Eq.symm <|
       sum_subset (β := R) (subset_univ ((sumCongrHom m n).range : Set (Perm (Sum m n))).toFinset) ?_
-    simp_rw [sum_mul_sum, ← sum_product', univ_product_univ]
-    refine sum_nbij (fun σ ↦ σ.fst.sumCongr σ.snd) ?_ ?_ ?_ ?_
-    · intro σ₁₂ _
-      simp only
-      erw [Set.mem_toFinset, MonoidHom.mem_range]
-      use σ₁₂
-      simp only [sumCongrHom_apply]
-    · intro σ₁ _ σ₂ _
-      dsimp only
-      intro h
-      have h2 : ∀ x, Perm.sumCongr σ₁.fst σ₁.snd x = Perm.sumCongr σ₂.fst σ₂.snd x :=
-        DFunLike.congr_fun h
-      simp only [Sum.map_inr, Sum.map_inl, Perm.sumCongr_apply, Sum.forall, Sum.inl.injEq,
-        Sum.inr.injEq] at h2
-      ext x
-      · exact h2.left x
-      · exact h2.right x
-    · intro σ hσ
-      erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ
-      obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
-      use σ₁₂
-      rw [← hσ₁₂]
-      simp
-    · simp only [forall_prop_of_true, Prod.forall, mem_univ]
-      intro σ₁ σ₂
-      rw [Fintype.prod_sum_type]
-      simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, fromBlocks_apply₁₁,
-        fromBlocks_apply₂₂]
-      rw [mul_mul_mul_comm]
-      congr
-      rw [sign_sumCongr, Units.val_mul, Int.cast_mul]
+    · simp_rw [sum_mul_sum, ← sum_product', univ_product_univ]
+      refine sum_nbij (fun σ ↦ σ.fst.sumCongr σ.snd) ?_ ?_ ?_ ?_
+      · intro σ₁₂ _
+        simp only
+        erw [Set.mem_toFinset, MonoidHom.mem_range]
+        use σ₁₂
+        simp only [sumCongrHom_apply]
+      · intro σ₁ _ σ₂ _
+        dsimp only
+        intro h
+        have h2 : ∀ x, Perm.sumCongr σ₁.fst σ₁.snd x = Perm.sumCongr σ₂.fst σ₂.snd x :=
+          DFunLike.congr_fun h
+        simp only [Sum.map_inr, Sum.map_inl, Perm.sumCongr_apply, Sum.forall, Sum.inl.injEq,
+          Sum.inr.injEq] at h2
+        ext x
+        · exact h2.left x
+        · exact h2.right x
+      · intro σ hσ
+        erw [Set.mem_toFinset, MonoidHom.mem_range] at hσ
+        obtain ⟨σ₁₂, hσ₁₂⟩ := hσ
+        use σ₁₂
+        rw [← hσ₁₂]
+        simp
+      · simp only [forall_prop_of_true, Prod.forall, mem_univ]
+        intro σ₁ σ₂
+        rw [Fintype.prod_sum_type]
+        simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, fromBlocks_apply₁₁,
+          fromBlocks_apply₂₂]
+        rw [mul_mul_mul_comm]
+        congr
+        rw [sign_sumCongr, Units.val_mul, Int.cast_mul]
     · rintro σ - hσn
       have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) := by
         rw [Set.mem_toFinset] at hσn

c3019c79

chore: split Algebra.Algebra.Basic (#12486)

Splits Algebra.Algebra.Defs off Algebra.Algebra.Basic. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Algebra.Basic is now a grab-bag of unrelated results, and should probably be split further or rehomed.

This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Algebra.Basic.

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

d64b17d9

Diff

@@ -9,7 +9,7 @@ import Mathlib.Data.Matrix.Notation
 import Mathlib.Data.Fintype.BigOperators
 import Mathlib.GroupTheory.Perm.Fin
 import Mathlib.GroupTheory.Perm.Sign
-import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Defs
 import Mathlib.Tactic.Ring
 import Mathlib.LinearAlgebra.Alternating.Basic
 import Mathlib.LinearAlgebra.Pi

c3019c79

chore: backports from #11997, adaptations for nightly-2024-04-07 (#12176)

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

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

02293f49

Diff

@@ -760,7 +760,7 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
   congr
   rw [← det_permute, det_succ_row_zero]
   refine' Finset.sum_congr rfl fun j _ => _
-  rw [mul_assoc, Matrix.submatrix_apply, submatrix_submatrix, id_comp, Function.comp_def, id.def]
+  rw [mul_assoc, Matrix.submatrix_apply, submatrix_submatrix, id_comp, Function.comp_def, id]
   congr
   · rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_zero]
   · ext i' j'

c3019c79

chore: avoid id.def (adaptation for nightly-2024-03-27) (#11829)

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

b8a0f589

Diff

@@ -714,7 +714,7 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   refine' Finset.sum_congr rfl fun i _ => Fin.cases _ (fun i => _) i
   · simp only [Fin.prod_univ_succ, Matrix.det_apply, Finset.mul_sum,
       Equiv.Perm.decomposeFin_symm_apply_zero, Fin.val_zero, one_mul,
-      Equiv.Perm.decomposeFin.symm_sign, Equiv.swap_self, if_true, id.def, eq_self_iff_true,
+      Equiv.Perm.decomposeFin.symm_sign, Equiv.swap_self, if_true, id, eq_self_iff_true,
       Equiv.Perm.decomposeFin_symm_apply_succ, Fin.succAbove_zero, Equiv.coe_refl, pow_zero,
       mul_smul_comm, of_apply]
   -- `univ_perm_fin_succ` gives a different embedding of `Perm (Fin n)` into

c3019c79

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -280,7 +280,7 @@ theorem det_permutation (σ : Perm n) :
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
     det (c • A) = det ((diagonal fun _ => c) * A) := by rw [smul_eq_diagonal_mul]
-    _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
+    _ = det (diagonal fun _ => c) * det A := det_mul _ _
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
 #align matrix.det_smul Matrix.det_smul
 
@@ -434,7 +434,7 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     (hA : A = B * C) : det A = det B :=
   calc
     det A = det (B * C) := congr_arg _ hA
-    _ = det B * det C := (det_mul _ _)
+    _ = det B * det C := det_mul _ _
     _ = det B := by rw [hC, mul_one]
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
 
@@ -442,7 +442,7 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     (hA : A = C * B) : det A = det B :=
   calc
     det A = det (C * B) := congr_arg _ hA
-    _ = det C * det B := (det_mul _ _)
+    _ = det C * det B := det_mul _ _
     _ = det B := by rw [hC, one_mul]
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul

c3019c79

chore: remove mathport name: <expression> lines (#11928)

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

11431c65

Diff

@@ -53,7 +53,6 @@ open Matrix BigOperators
 variable {m n : Type*} [DecidableEq n] [Fintype n] [DecidableEq m] [Fintype m]
 variable {R : Type v} [CommRing R]
 
--- mathport name: «exprε »
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
 /-- `det` is an `AlternatingMap` in the rows of the matrix. -/

c3019c79

chore(Data/Matrix): add explicit of typecasts (#11593)

This adds some missing Matrix.of typecasts, and uses Matrix.submatrix in places where this is more reasonable than adding of.

Matrix.det_permute' is a new lemma that fills the obvious gap that these submatrix restatements emphasize.

25e680d5

Diff

@@ -238,10 +238,15 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det := by
 
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
-    (Matrix.det fun i => M (σ i)) = Perm.sign σ * M.det :=
+    (M.submatrix σ id).det = Perm.sign σ * M.det :=
   ((detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_perm M σ).trans (by simp [Units.smul_def])
 #align matrix.det_permute Matrix.det_permute
 
+/-- Permuting the rows changes the sign of the determinant. -/
+theorem det_permute' (σ : Perm n) (M : Matrix n n R) :
+    (M.submatrix id σ).det = Perm.sign σ * M.det := by
+  rw [← det_transpose, transpose_submatrix, det_permute, det_transpose]
+
 /-- Permuting rows and columns with the same equivalence has no effect. -/
 @[simp]
 theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) :
@@ -756,11 +761,12 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
   congr
   rw [← det_permute, det_succ_row_zero]
   refine' Finset.sum_congr rfl fun j _ => _
-  rw [mul_assoc, Matrix.submatrix, Matrix.submatrix]
+  rw [mul_assoc, Matrix.submatrix_apply, submatrix_submatrix, id_comp, Function.comp_def, id.def]
   congr
   · rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_zero]
   · ext i' j'
-    rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_succ]
+    rw [Equiv.Perm.inv_def, Matrix.submatrix_apply, Matrix.submatrix_apply,
+      Fin.cycleRange_symm_succ]
 #align matrix.det_succ_row Matrix.det_succ_row
 
 /-- Laplacian expansion of the determinant of an `n+1 × n+1` matrix along column `j`. -/

c3019c79

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -717,8 +717,8 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   -- `Perm (Fin n.succ)` than the determinant of the submatrix we want,
   -- permute `A` so that we get the correct one.
   have : (-1 : R) ^ (i : ℕ) = (Perm.sign i.cycleRange) := by simp [Fin.sign_cycleRange]
-  rw [Fin.val_succ, pow_succ, this, mul_assoc, mul_assoc, mul_left_comm (ε _), ←
-    det_permute, Matrix.det_apply, Finset.mul_sum, Finset.mul_sum]
+  rw [Fin.val_succ, pow_succ', this, mul_assoc, mul_assoc, mul_left_comm (ε _),
+    ← det_permute, Matrix.det_apply, Finset.mul_sum, Finset.mul_sum]
   -- now we just need to move the corresponding parts to the same place
   refine' Finset.sum_congr rfl fun σ _ => _
   rw [Equiv.Perm.decomposeFin.symm_sign, if_neg (Fin.succ_ne_zero i)]

c3019c79

chore(*): migrate from RingHom.map_* to _root_.map_* (#11660)

Cherry-picked from #9607 Co-authored-by: @semorrison

859f3760

Diff

@@ -326,7 +326,7 @@ variable {S : Type w} [CommRing S]
 
 theorem _root_.RingHom.map_det (f : R →+* S) (M : Matrix n n R) :
     f M.det = Matrix.det (f.mapMatrix M) :=
-  by simp [Matrix.det_apply', f.map_sum, f.map_prod]
+  by simp [Matrix.det_apply', map_sum f, map_prod f]
 #align ring_hom.map_det RingHom.map_det
 
 theorem _root_.RingEquiv.map_det (f : R ≃+* S) (M : Matrix n n R) :

c3019c79

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -51,7 +51,6 @@ namespace Matrix
 open Matrix BigOperators
 
 variable {m n : Type*} [DecidableEq n] [Fintype n] [DecidableEq m] [Fintype m]
-
 variable {R : Type v} [CommRing R]
 
 -- mathport name: «exprε »

c3019c79

fix: denote alternating map by ⋀, not Λ (#11064)

That is, \bigwedge, not \Lambda

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>

008d6e96

Diff

@@ -58,7 +58,7 @@ variable {R : Type v} [CommRing R]
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
 /-- `det` is an `AlternatingMap` in the rows of the matrix. -/
-def detRowAlternating : (n → R) [Λ^n]→ₗ[R] R :=
+def detRowAlternating : (n → R) [⋀^n]→ₗ[R] R :=
   MultilinearMap.alternatization ((MultilinearMap.mkPiAlgebra R n R).compLinearMap LinearMap.proj)
 #align matrix.det_row_alternating Matrix.detRowAlternating
 
@@ -91,7 +91,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
 
 -- @[simp] -- Porting note (#10618): simp can prove this
 theorem det_zero (_ : Nonempty n) : det (0 : Matrix n n R) = 0 :=
-  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_zero
+  (detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_zero
 #align matrix.det_zero Matrix.det_zero
 
 @[simp]
@@ -240,7 +240,7 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det := by
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = Perm.sign σ * M.det :=
-  ((detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_perm M σ).trans (by simp [Units.smul_def])
+  ((detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_perm M σ).trans (by simp [Units.smul_def])
 #align matrix.det_permute Matrix.det_permute
 
 /-- Permuting rows and columns with the same equivalence has no effect. -/
@@ -362,7 +362,7 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 
 
 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
-  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_coord_zero i (funext h)
+  (detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
 
 theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) :
@@ -375,7 +375,7 @@ variable {M : Matrix n n R} {i j : n}
 
 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
-  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_eq_zero_of_eq M hij i_ne_j
+  (detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_eq_zero_of_eq M hij i_ne_j
 #align matrix.det_zero_of_row_eq Matrix.det_zero_of_row_eq
 
 /-- If a matrix has a repeated column, the determinant will be zero. -/
@@ -388,7 +388,7 @@ end DetZero
 
 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
-  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_add M j u v
+  (detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_add M j u v
 #align matrix.det_update_row_add Matrix.det_updateRow_add
 
 theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
@@ -399,7 +399,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
 
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
-  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_smul M j s u
+  (detRowAlternating : (n → R) [⋀^n]→ₗ[R] R).map_smul M j s u
 #align matrix.det_update_row_smul Matrix.det_updateRow_smul
 
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :

c3019c79

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -89,7 +89,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem det_zero (_ : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_zero
 #align matrix.det_zero Matrix.det_zero

c3019c79

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -13,6 +13,7 @@ import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Tactic.Ring
 import Mathlib.LinearAlgebra.Alternating.Basic
 import Mathlib.LinearAlgebra.Pi
+import Mathlib.GroupTheory.GroupAction.Ring
 
 #align_import linear_algebra.matrix.determinant from "leanprover-community/mathlib"@"c3019c79074b0619edb4b27553a91b2e82242395"

c3019c79

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -658,7 +658,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       dsimp only
       intro h
       have h2 : ∀ x, Perm.sumCongr σ₁.fst σ₁.snd x = Perm.sumCongr σ₂.fst σ₂.snd x :=
-        FunLike.congr_fun h
+        DFunLike.congr_fun h
       simp only [Sum.map_inr, Sum.map_inl, Perm.sumCongr_apply, Sum.forall, Sum.inl.injEq,
         Sum.inr.injEq] at h2
       ext x

c3019c79

chore: Relocate big operator lemmas (#9383)

A bunch of lemmas in Algebra.BigOperators.Ring were not about rings. This PR moves them along with some lemmas from Data.Fintype.BigOperators to their correct place.

I create a new file with the content from #6605 to avoid importing Fin material in finset files as a result.

From LeanAPAP

b8dc3667

Diff

@@ -647,8 +647,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     simp_rw [det_apply']
     convert Eq.symm <|
       sum_subset (β := R) (subset_univ ((sumCongrHom m n).range : Set (Perm (Sum m n))).toFinset) ?_
-    rw [sum_mul_sum]
-    simp_rw [univ_product_univ]
+    simp_rw [sum_mul_sum, ← sum_product', univ_product_univ]
     refine sum_nbij (fun σ ↦ σ.fst.sumCongr σ.snd) ?_ ?_ ?_ ?_
     · intro σ₁₂ _
       simp only

c3019c79

feat: Better lemmas for transferring finite sums along equivalences (#9237)

Lemmas around this were a mess, throth in terms of names, statement and location. This PR standardises everything to be in Algebra.BigOperators.Basic and changes the lemmas to take in InjOn and SurjOn assumptions where possible (and where impossible make sure the hypotheses are taken in the correct order) and moves the equality of functions hypothesis last.

Also add a few lemmas that help fix downstream uses by golfing.

From LeanAPAP and LeanCamCombi

82c60323

Diff

@@ -160,9 +160,9 @@ theorem det_mul (M N : Matrix n n R) : det (M * N) = det M * det N :=
         sum_subset (filter_subset _ _) fun f _ hbij =>
           det_mul_aux <| by simpa only [true_and_iff, mem_filter, mem_univ] using hbij)
     _ = ∑ τ : Perm n, ∑ σ : Perm n, ε σ * ∏ i, M (σ i) (τ i) * N (τ i) i :=
-      (sum_bij (fun p h => Equiv.ofBijective p (mem_filter.1 h).2) (fun _ _ => mem_univ _)
-        (fun _ _ => rfl) (fun _ _ _ _ h => by injection h) fun b _ =>
-        ⟨b, mem_filter.2 ⟨mem_univ _, b.bijective⟩, coe_fn_injective rfl⟩)
+      sum_bij (fun p h ↦ Equiv.ofBijective p (mem_filter.1 h).2) (fun _ _ ↦ mem_univ _)
+        (fun _ _ _ _ h ↦ by injection h)
+        (fun b _ ↦ ⟨b, mem_filter.2 ⟨mem_univ _, b.bijective⟩, coe_fn_injective rfl⟩) fun _ _ ↦ rfl
     _ = ∑ σ : Perm n, ∑ τ : Perm n, (∏ i, N (σ i) i) * ε τ * ∏ j, M (τ j) (σ j) := by
       simp only [mul_comm, mul_left_comm, prod_mul_distrib, mul_assoc]
     _ = ∑ σ : Perm n, ∑ τ : Perm n, (∏ i, N (σ i) i) * (ε σ * ε τ) * ∏ i, M (τ i) i :=
@@ -585,19 +585,12 @@ theorem det_blockDiagonal {o : Type*} [Fintype o] [DecidableEq o] (M : o → Mat
     Finset.mem_filter.trans ⟨fun h => h.2, fun h => ⟨Finset.mem_univ _, h⟩⟩
   rw [← Finset.sum_subset (Finset.subset_univ preserving_snd) _]
   -- And that these are in bijection with `o → Equiv.Perm m`.
-  rw [(Finset.sum_bij
-        (fun (σ : ∀ k : o, k ∈ Finset.univ → Equiv.Perm n) _ =>
-          prodCongrLeft fun k => σ k (Finset.mem_univ k))
-        _ _ _ _).symm]
+  refine (Finset.sum_bij (fun σ _ => prodCongrLeft fun k ↦ σ k (mem_univ k)) ?_ ?_ ?_ ?_).symm
   · intro σ _
     rw [mem_preserving_snd]
     rintro ⟨-, x⟩
     simp only [prodCongrLeft_apply]
-  · intro σ _
-    rw [Finset.prod_mul_distrib, ← Finset.univ_product_univ, Finset.prod_product_right]
-    simp only [sign_prodCongrLeft, Units.coe_prod, Int.cast_prod, blockDiagonal_apply_eq,
-      prodCongrLeft_apply]
-  · intro σ σ' _ _ eq
+  · intro σ _ σ' _ eq
     ext x hx k
     simp only at eq
     have :
@@ -632,6 +625,10 @@ theorem det_blockDiagonal {o : Type*} [Fintype o] [DecidableEq o] (M : o → Mat
     · ext ⟨k, x⟩
       · simp only [coe_fn_mk, prodCongrLeft_apply]
       · simp only [prodCongrLeft_apply, hσ]
+  · intro σ _
+    rw [Finset.prod_mul_distrib, ← Finset.univ_product_univ, Finset.prod_product_right]
+    simp only [sign_prodCongrLeft, Units.coe_prod, Int.cast_prod, blockDiagonal_apply_eq,
+      prodCongrLeft_apply]
   · intro σ _ hσ
     rw [mem_preserving_snd] at hσ
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
@@ -652,21 +649,13 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       sum_subset (β := R) (subset_univ ((sumCongrHom m n).range : Set (Perm (Sum m n))).toFinset) ?_
     rw [sum_mul_sum]
     simp_rw [univ_product_univ]
-    rw [(sum_bij (fun (σ : Perm m × Perm n) _ => Equiv.sumCongr σ.fst σ.snd) _ _ _ _).symm]
-    · intro σ₁₂ h
+    refine sum_nbij (fun σ ↦ σ.fst.sumCongr σ.snd) ?_ ?_ ?_ ?_
+    · intro σ₁₂ _
       simp only
       erw [Set.mem_toFinset, MonoidHom.mem_range]
       use σ₁₂
       simp only [sumCongrHom_apply]
-    · simp only [forall_prop_of_true, Prod.forall, mem_univ]
-      intro σ₁ σ₂
-      rw [Fintype.prod_sum_type]
-      simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, fromBlocks_apply₁₁,
-        fromBlocks_apply₂₂]
-      rw [mul_mul_mul_comm]
-      congr
-      rw [sign_sumCongr, Units.val_mul, Int.cast_mul]
-    · intro σ₁ σ₂ h₁ h₂
+    · intro σ₁ _ σ₂ _
       dsimp only
       intro h
       have h2 : ∀ x, Perm.sumCongr σ₁.fst σ₁.snd x = Perm.sumCongr σ₂.fst σ₂.snd x :=
@@ -682,6 +671,14 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       use σ₁₂
       rw [← hσ₁₂]
       simp
+    · simp only [forall_prop_of_true, Prod.forall, mem_univ]
+      intro σ₁ σ₂
+      rw [Fintype.prod_sum_type]
+      simp_rw [Equiv.sumCongr_apply, Sum.map_inr, Sum.map_inl, fromBlocks_apply₁₁,
+        fromBlocks_apply₂₂]
+      rw [mul_mul_mul_comm]
+      congr
+      rw [sign_sumCongr, Units.val_mul, Int.cast_mul]
     · rintro σ - hσn
       have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) := by
         rw [Set.mem_toFinset] at hσn

c3019c79

chore: introduce notation for AlternatingMap (#8697)

Use M [Λ^ι]→ₗ[R] N for AlternatingMap R M N ι, similarly to the existing notation M [Λ^ι]→L[R] N for ContinuousAlternatingMap R M N ι.

ae010c18

Diff

@@ -57,7 +57,7 @@ variable {R : Type v} [CommRing R]
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
 /-- `det` is an `AlternatingMap` in the rows of the matrix. -/
-def detRowAlternating : AlternatingMap R (n → R) R n :=
+def detRowAlternating : (n → R) [Λ^n]→ₗ[R] R :=
   MultilinearMap.alternatization ((MultilinearMap.mkPiAlgebra R n R).compLinearMap LinearMap.proj)
 #align matrix.det_row_alternating Matrix.detRowAlternating
 
@@ -90,7 +90,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
 
 -- @[simp] -- Porting note: simp can prove this
 theorem det_zero (_ : Nonempty n) : det (0 : Matrix n n R) = 0 :=
-  (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
+  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_zero
 #align matrix.det_zero Matrix.det_zero
 
 @[simp]
@@ -239,7 +239,7 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det := by
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = Perm.sign σ * M.det :=
-  ((detRowAlternating : AlternatingMap R (n → R) R n).map_perm M σ).trans (by simp [Units.smul_def])
+  ((detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_perm M σ).trans (by simp [Units.smul_def])
 #align matrix.det_permute Matrix.det_permute
 
 /-- Permuting rows and columns with the same equivalence has no effect. -/
@@ -361,7 +361,7 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 
 
 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
-  (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
+  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
 
 theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) :
@@ -374,7 +374,7 @@ variable {M : Matrix n n R} {i j : n}
 
 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
-  (detRowAlternating : AlternatingMap R (n → R) R n).map_eq_zero_of_eq M hij i_ne_j
+  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_eq_zero_of_eq M hij i_ne_j
 #align matrix.det_zero_of_row_eq Matrix.det_zero_of_row_eq
 
 /-- If a matrix has a repeated column, the determinant will be zero. -/
@@ -387,7 +387,7 @@ end DetZero
 
 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
-  (detRowAlternating : AlternatingMap R (n → R) R n).map_add M j u v
+  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_add M j u v
 #align matrix.det_update_row_add Matrix.det_updateRow_add
 
 theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
@@ -398,7 +398,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
 
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
-  (detRowAlternating : AlternatingMap R (n → R) R n).map_smul M j s u
+  (detRowAlternating : (n → R) [Λ^n]→ₗ[R] R).map_smul M j s u
 #align matrix.det_update_row_smul Matrix.det_updateRow_smul
 
 theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :

c3019c79

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -793,7 +793,9 @@ theorem det_fin_one_of (a : R) : det !![a] = a :=
 
 /-- Determinant of 2x2 matrix -/
 theorem det_fin_two (A : Matrix (Fin 2) (Fin 2) R) : det A = A 0 0 * A 1 1 - A 0 1 * A 1 0 := by
-  simp [Matrix.det_succ_row_zero, Fin.sum_univ_succ]
+  simp only [det_succ_row_zero, det_unique, Fin.default_eq_zero, submatrix_apply,
+    Fin.succ_zero_eq_one, Fin.sum_univ_succ, Fin.val_zero, Fin.zero_succAbove, univ_unique,
+    Fin.val_succ, Fin.coe_fin_one, Fin.succ_succAbove_zero, sum_singleton]
   ring
 #align matrix.det_fin_two Matrix.det_fin_two
 
@@ -805,11 +807,13 @@ theorem det_fin_two_of (a b c d : R) : Matrix.det !![a, b; c, d] = a * d - b * c
 /-- Determinant of 3x3 matrix -/
 theorem det_fin_three (A : Matrix (Fin 3) (Fin 3) R) :
     det A =
-      A 0 0 * A 1 1 * A 2 2 - A 0 0 * A 1 2 * A 2 1 - A 0 1 * A 1 0 * A 2 2 +
-            A 0 1 * A 1 2 * A 2 0 +
-          A 0 2 * A 1 0 * A 2 1 -
-        A 0 2 * A 1 1 * A 2 0 := by
-  simp [Matrix.det_succ_row_zero, Fin.sum_univ_succ]
+      A 0 0 * A 1 1 * A 2 2 - A 0 0 * A 1 2 * A 2 1
+      - A 0 1 * A 1 0 * A 2 2 + A 0 1 * A 1 2 * A 2 0
+      + A 0 2 * A 1 0 * A 2 1 - A 0 2 * A 1 1 * A 2 0 := by
+  simp only [det_succ_row_zero, Nat.odd_iff_not_even, submatrix_apply, Fin.succ_zero_eq_one,
+    submatrix_submatrix, det_unique, Fin.default_eq_zero, comp_apply, Fin.succ_one_eq_two,
+    Fin.sum_univ_succ, Fin.val_zero, Fin.zero_succAbove, univ_unique, Fin.val_succ,
+    Fin.coe_fin_one, Fin.succ_succAbove_zero, sum_singleton, Fin.succ_succAbove_one, even_add_self]
   ring
 #align matrix.det_fin_three Matrix.det_fin_three

c3019c79

chore: swap primes on forall_apply_eq_imp_iff (#7705)

Two pairs of the form foo and foo', where foo' is the simp lemma (and hence used in many simp onlys) and foo is not used at all.

Swap the primes, so that when it is time (now!) to upstream the lemma we actually use, it doesn't need to have a prime...

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

2da494d2

Diff

@@ -686,7 +686,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       have h1 : ¬∀ x, ∃ y, Sum.inl y = σ (Sum.inl x) := by
         rw [Set.mem_toFinset] at hσn
         -- Porting note: golfed
-        simpa only [Set.MapsTo, Set.mem_range, forall_exists_index, forall_apply_eq_imp_iff'] using
+        simpa only [Set.MapsTo, Set.mem_range, forall_exists_index, forall_apply_eq_imp_iff] using
           mt mem_sumCongrHom_range_of_perm_mapsTo_inl hσn
       obtain ⟨a, ha⟩ := not_forall.mp h1
       cases' hx : σ (Sum.inl a) with a2 b

c3019c79

chore: fix deprecated identifier (#7502)

I came across a few places in Mathlib that still used this name that has been deprecated for a few years now. Now we're consistent again and I don't have to suffer when encountering the wrong version :)

a5516f58

Diff

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Kenny Lau, Chris Hughes, Tim Baanen
+Authors: Kenny Lau, Chris Hughes, Anne Baanen
 -/
 import Mathlib.Data.Matrix.PEquiv
 import Mathlib.Data.Matrix.Block

c3019c79

chore(LinearAlgebra/Alternating): split (#7448)

I'm going to refactor/expand API about domCoprod, and I don't want to rebuild the whole library when I do it.

d36df78d

Diff

@@ -11,7 +11,7 @@ import Mathlib.GroupTheory.Perm.Fin
 import Mathlib.GroupTheory.Perm.Sign
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Tactic.Ring
-import Mathlib.LinearAlgebra.Alternating
+import Mathlib.LinearAlgebra.Alternating.Basic
 import Mathlib.LinearAlgebra.Pi
 
 #align_import linear_algebra.matrix.determinant from "leanprover-community/mathlib"@"c3019c79074b0619edb4b27553a91b2e82242395"

c3019c79

chore: make fields of algebraic (iso)morphisms protected (#7150)

Pretty much all these fields are implementation details, and not intended as API. There is no point in open MonoidHom bringing toFun or map_mul' into the environment, as neither are the preferred way to spell those things.

fbed0880

Diff

@@ -669,9 +669,8 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
     · intro σ₁ σ₂ h₁ h₂
       dsimp only
       intro h
-      have h2 : ∀ x, Perm.sumCongr σ₁.fst σ₁.snd x = Perm.sumCongr σ₂.fst σ₂.snd x := by
-        intro x
-        exact congr_fun (congr_arg toFun h) x
+      have h2 : ∀ x, Perm.sumCongr σ₁.fst σ₁.snd x = Perm.sumCongr σ₂.fst σ₂.snd x :=
+        FunLike.congr_fun h
       simp only [Sum.map_inr, Sum.map_inl, Perm.sumCongr_apply, Sum.forall, Sum.inl.injEq,
         Sum.inr.injEq] at h2
       ext x

c3019c79

chore: update/remove heart beat bumps (#6860)

We clean up heart beat bumps after #6474.

c95f05bd

Diff

@@ -147,8 +147,6 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
       mul_swap_involutive i j σ
 #align matrix.det_mul_aux Matrix.det_mul_aux
 
--- Porting note: need to bump for last simp; new after #3414 (reenableeta)
-set_option maxHeartbeats 300000 in
 @[simp]
 theorem det_mul (M N : Matrix n n R) : det (M * N) = det M * det N :=
   calc

c3019c79

chore: cleanup Mathlib.Init.Data.Prod (#6972)

Removing from Mathlib.Init.Data.Prod from the early parts of the import hierarchy.

While at it, remove unnecessary uses of Prod.mk.eta across the library.

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

b5528b3b

Diff

@@ -638,7 +638,7 @@ theorem det_blockDiagonal {o : Type*} [Fintype o] [DecidableEq o] (M : o → Mat
     rw [mem_preserving_snd] at hσ
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
     rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), mul_zero]
-    rw [← @Prod.mk.eta _ _ (σ (k, x)), blockDiagonal_apply_ne]
+    rw [blockDiagonal_apply_ne]
     exact hkx
 #align matrix.det_block_diagonal Matrix.det_blockDiagonal

c3019c79

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

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).

277dea95

Diff

@@ -81,7 +81,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
   refine' (Finset.sum_eq_single 1 _ _).trans _
   · rintro σ - h2
     cases' not_forall.1 (mt Equiv.ext h2) with x h3
-    convert MulZeroClass.mul_zero (ε σ)
+    convert mul_zero (ε σ)
     apply Finset.prod_eq_zero (mem_univ x)
     exact if_neg h3
   · simp
@@ -481,7 +481,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       simp [hs]
     congr
     ext i j
-    rw [A_eq, this, MulZeroClass.zero_mul, add_zero]
+    rw [A_eq, this, zero_mul, add_zero]
   | @insert i s _hi ih =>
     intro c hs k hk A_eq
     have hAi : A i = B i + c i • B k := funext (A_eq i)
@@ -521,7 +521,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · congr
     ext i j
     refine' Fin.cases (h0 j) (fun i => _) i
-    rw [hsucc, hc i (Fin.succ_pos _), MulZeroClass.zero_mul, add_zero]
+    rw [hsucc, hc i (Fin.succ_pos _), zero_mul, add_zero]
   set M' := updateRow M k.succ (N k.succ) with hM'
   have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSucc k)) := by
     ext i j
@@ -541,7 +541,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   intro i j
   rw [Function.update_apply]
   split_ifs with hik
-  · rw [MulZeroClass.zero_mul, add_zero, hM', hik, updateRow_self]
+  · rw [zero_mul, add_zero, hM', hik, updateRow_self]
   rw [hM', updateRow_ne ((Fin.succ_injective _).ne hik), hsucc]
   by_cases hik2 : k < i
   · simp [hc i (Fin.succ_lt_succ_iff.mpr hik2)]
@@ -637,7 +637,7 @@ theorem det_blockDiagonal {o : Type*} [Fintype o] [DecidableEq o] (M : o → Mat
   · intro σ _ hσ
     rw [mem_preserving_snd] at hσ
     obtain ⟨⟨k, x⟩, hkx⟩ := not_forall.mp hσ
-    rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), MulZeroClass.mul_zero]
+    rw [Finset.prod_eq_zero (Finset.mem_univ (k, x)), mul_zero]
     rw [← @Prod.mk.eta _ _ (σ (k, x)), blockDiagonal_apply_ne]
     exact hkx
 #align matrix.det_block_diagonal Matrix.det_blockDiagonal
@@ -695,7 +695,7 @@ theorem det_fromBlocks_zero₂₁ (A : Matrix m m R) (B : Matrix m n R) (D : Mat
       cases' hx : σ (Sum.inl a) with a2 b
       · have hn := (not_exists.mp ha) a2
         exact absurd hx.symm hn
-      · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), MulZeroClass.mul_zero]
+      · rw [Finset.prod_eq_zero (Finset.mem_univ (Sum.inl a)), mul_zero]
         rw [hx, fromBlocks_apply₂₁, zero_apply]
 #align matrix.det_from_blocks_zero₂₁ Matrix.det_fromBlocks_zero₂₁

c3019c79

refactor(Data/Matrix): Eliminate ⬝ notation in favor of HMul (#6487)

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).

38c07226

Diff

@@ -28,7 +28,7 @@ This file defines the determinant of a matrix, `Matrix.det`, and its essential p
 
 ## Main results
 
- - `det_mul`: the determinant of `A ⬝ B` is the product of determinants
+ - `det_mul`: the determinant of `A * B` is the product of determinants
  - `det_zero_of_row_eq`: the determinant is zero if there is a repeated row
  - `det_block_diagonal`: the determinant of a block diagonal matrix is a product
    of the blocks' determinants
@@ -150,9 +150,9 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
 -- Porting note: need to bump for last simp; new after #3414 (reenableeta)
 set_option maxHeartbeats 300000 in
 @[simp]
-theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
+theorem det_mul (M N : Matrix n n R) : det (M * N) = det M * det N :=
   calc
-    det (M ⬝ N) = ∑ p : n → n, ∑ σ : Perm n, ε σ * ∏ i, M (σ i) (p i) * N (p i) i := by
+    det (M * N) = ∑ p : n → n, ∑ σ : Perm n, ε σ * ∏ i, M (σ i) (p i) * N (p i) i := by
       simp only [det_apply', mul_apply, prod_univ_sum, mul_sum, Fintype.piFinset_univ]
       rw [Finset.sum_comm]
     _ =
@@ -199,27 +199,29 @@ theorem coe_detMonoidHom : (detMonoidHom : Matrix n n R → R) = det :=
 #align matrix.coe_det_monoid_hom Matrix.coe_detMonoidHom
 
 /-- On square matrices, `mul_comm` applies under `det`. -/
-theorem det_mul_comm (M N : Matrix m m R) : det (M ⬝ N) = det (N ⬝ M) := by
+theorem det_mul_comm (M N : Matrix m m R) : det (M * N) = det (N * M) := by
   rw [det_mul, det_mul, mul_comm]
 #align matrix.det_mul_comm Matrix.det_mul_comm
 
 /-- On square matrices, `mul_left_comm` applies under `det`. -/
-theorem det_mul_left_comm (M N P : Matrix m m R) : det (M ⬝ (N ⬝ P)) = det (N ⬝ (M ⬝ P)) := by
+theorem det_mul_left_comm (M N P : Matrix m m R) : det (M * (N * P)) = det (N * (M * P)) := by
   rw [← Matrix.mul_assoc, ← Matrix.mul_assoc, det_mul, det_mul_comm M N, ← det_mul]
 #align matrix.det_mul_left_comm Matrix.det_mul_left_comm
 
 /-- On square matrices, `mul_right_comm` applies under `det`. -/
-theorem det_mul_right_comm (M N P : Matrix m m R) : det (M ⬝ N ⬝ P) = det (M ⬝ P ⬝ N) := by
+theorem det_mul_right_comm (M N P : Matrix m m R) : det (M * N * P) = det (M * P * N) := by
   rw [Matrix.mul_assoc, Matrix.mul_assoc, det_mul, det_mul_comm N P, ← det_mul]
 #align matrix.det_mul_right_comm Matrix.det_mul_right_comm
 
+-- TODO(mathlib4#6607): fix elaboration so that the ascription isn't needed
 theorem det_units_conj (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
-    det (↑M ⬝ N ⬝ ↑M⁻¹ : Matrix m m R) = det N := by
-  rw [det_mul_right_comm, ← mul_eq_mul, ← mul_eq_mul, Units.mul_inv, one_mul]
+    det ((M : Matrix _ _ _) * N * (↑M⁻¹ : Matrix _ _ _)) = det N := by
+  rw [det_mul_right_comm, Units.mul_inv, one_mul]
 #align matrix.det_units_conj Matrix.det_units_conj
 
+-- TODO(mathlib4#6607): fix elaboration so that the ascription isn't needed
 theorem det_units_conj' (M : (Matrix m m R)ˣ) (N : Matrix m m R) :
-    det (↑M⁻¹ ⬝ N ⬝ ↑M : Matrix m m R) = det N :=
+    det ((↑M⁻¹ : Matrix _ _ _) * N * (↑M : Matrix _ _ _)) = det N :=
   det_units_conj M⁻¹ N
 #align matrix.det_units_conj' Matrix.det_units_conj'
 
@@ -275,7 +277,7 @@ theorem det_permutation (σ : Perm n) :
 
 theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n * det A :=
   calc
-    det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
+    det (c • A) = det ((diagonal fun _ => c) * A) := by rw [smul_eq_diagonal_mul]
     _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
 #align matrix.det_smul Matrix.det_smul
@@ -301,7 +303,7 @@ the product of the `v`s. -/
 theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     det (of fun i j => v j * A i j) = (∏ i, v i) * det A :=
   calc
-    det (of fun i j => v j * A i j) = det (A ⬝ diagonal v) :=
+    det (of fun i j => v j * A i j) = det (A * diagonal v) :=
       congr_arg det <| by
         ext
         simp [mul_comm]
@@ -427,17 +429,17 @@ Lemmas showing the determinant is invariant under a variety of operations.
 
 
 theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
-    (hA : A = B ⬝ C) : det A = det B :=
+    (hA : A = B * C) : det A = det B :=
   calc
-    det A = det (B ⬝ C) := congr_arg _ hA
+    det A = det (B * C) := congr_arg _ hA
     _ = det B * det C := (det_mul _ _)
     _ = det B := by rw [hC, mul_one]
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
 
 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
-    (hA : A = C ⬝ B) : det A = det B :=
+    (hA : A = C * B) : det A = det B :=
   calc
-    det A = det (C ⬝ B) := congr_arg _ hA
+    det A = det (C * B) := congr_arg _ hA
     _ = det C * det B := (det_mul _ _)
     _ = det B := by rw [hC, one_mul]
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul

c3019c79

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -49,7 +49,7 @@ namespace Matrix
 
 open Matrix BigOperators
 
-variable {m n : Type _} [DecidableEq n] [Fintype n] [DecidableEq m] [Fintype m]
+variable {m n : Type*} [DecidableEq n] [Fintype n] [DecidableEq m] [Fintype m]
 
 variable {R : Type v} [CommRing R]
 
@@ -115,7 +115,7 @@ theorem det_eq_one_of_card_eq_zero {A : Matrix n n R} (h : Fintype.card n = 0) :
 Although `Unique` implies `DecidableEq` and `Fintype`, the instances might
 not be syntactically equal. Thus, we need to fill in the args explicitly. -/
 @[simp]
-theorem det_unique {n : Type _} [Unique n] [DecidableEq n] [Fintype n] (A : Matrix n n R) :
+theorem det_unique {n : Type*} [Unique n] [DecidableEq n] [Fintype n] (A : Matrix n n R) :
     det A = A default default := by simp [det_apply, univ_unique]
 #align matrix.det_unique Matrix.det_unique
 
@@ -569,7 +569,7 @@ theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 end DetEq
 
 @[simp]
-theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Matrix n n R) :
+theorem det_blockDiagonal {o : Type*} [Fintype o] [DecidableEq o] (M : o → Matrix n n R) :
     (blockDiagonal M).det = ∏ k, (M k).det := by
   -- Rewrite the determinants as a sum over permutations.
   simp_rw [det_apply']

c3019c79

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Chris Hughes, Tim Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.determinant
-! leanprover-community/mathlib commit c3019c79074b0619edb4b27553a91b2e82242395
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Matrix.PEquiv
 import Mathlib.Data.Matrix.Block
@@ -19,6 +14,8 @@ import Mathlib.Tactic.Ring
 import Mathlib.LinearAlgebra.Alternating
 import Mathlib.LinearAlgebra.Pi
 
+#align_import linear_algebra.matrix.determinant from "leanprover-community/mathlib"@"c3019c79074b0619edb4b27553a91b2e82242395"
+
 /-!
 # Determinant of a matrix

c3019c79

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -486,7 +486,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
   | @insert i s _hi ih =>
     intro c hs k hk A_eq
     have hAi : A i = B i + c i • B k := funext (A_eq i)
-    rw [@ih (updateRow  B i (A i)) (Function.update c i 0), hAi, det_updateRow_add_smul_self]
+    rw [@ih (updateRow B i (A i)) (Function.update c i 0), hAi, det_updateRow_add_smul_self]
     · exact mt (fun h => show k ∈ insert i s from h ▸ Finset.mem_insert_self _ _) hk
     · intro i' hi'
       rw [Function.update_apply]

c3019c79

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -91,7 +91,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
 
-@[simp]
+-- @[simp] -- Porting note: simp can prove this
 theorem det_zero (_ : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
 #align matrix.det_zero Matrix.det_zero
@@ -516,7 +516,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (_hc : ∀ i : Fin n, k < i.succ → c i = 0)
       {M N : Matrix (Fin n.succ) (Fin n.succ) R} (_h0 : ∀ j, M 0 j = N 0 j)
-      (_hsucc : ∀ (i : Fin n) (j), M i.succ j = N i.succ j + c i * M (Fin.castSuccEmb i) j),
+      (_hsucc : ∀ (i : Fin n) (j), M i.succ j = N i.succ j + c i * M (Fin.castSucc i) j),
       det M = det N := by
   refine' Fin.induction _ (fun k ih => _) k <;> intro c hc M N h0 hsucc
   · congr
@@ -524,16 +524,16 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     refine' Fin.cases (h0 j) (fun i => _) i
     rw [hsucc, hc i (Fin.succ_pos _), MulZeroClass.zero_mul, add_zero]
   set M' := updateRow M k.succ (N k.succ) with hM'
-  have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSuccEmb k)) := by
+  have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSucc k)) := by
     ext i j
     by_cases hi : i = k.succ
     · simp [hi, hM', hsucc, updateRow_self]
     rw [updateRow_ne hi, hM', updateRow_ne hi]
-  have k_ne_succ : (Fin.castSuccEmb k) ≠ k.succ := (Fin.castSuccEmb_lt_succ k).ne
-  have M_k : M (Fin.castSuccEmb k) = M' (Fin.castSuccEmb k) := (updateRow_ne k_ne_succ).symm
+  have k_ne_succ : (Fin.castSucc k) ≠ k.succ := (Fin.castSucc_lt_succ k).ne
+  have M_k : M (Fin.castSucc k) = M' (Fin.castSucc k) := (updateRow_ne k_ne_succ).symm
   rw [hM, M_k, det_updateRow_add_smul_self M' k_ne_succ.symm, ih (Function.update c k 0)]
   · intro i hi
-    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff] at hi
+    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi
     rw [Function.update_apply]
     split_ifs with hik
     · rfl
@@ -548,13 +548,13 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · simp [hc i (Fin.succ_lt_succ_iff.mpr hik2)]
   rw [updateRow_ne]
   apply ne_of_lt
-  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
+  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ j, A 0 j = B 0 j)
-    (A_succ : ∀ (i : Fin n) (j), A i.succ j = B i.succ j + c i * A (Fin.castSuccEmb i) j) :
+    (A_succ : ∀ (i : Fin n) (j), A i.succ j = B i.succ j + c i * A (Fin.castSucc i) j) :
     det A = det B :=
   det_eq_of_forall_row_eq_smul_add_pred_aux (Fin.last _) c
     (fun _ hi => absurd hi (not_lt_of_ge (Fin.le_last _))) A_zero A_succ
@@ -563,7 +563,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ i, A i 0 = B i 0)
-    (A_succ : ∀ (i) (j : Fin n), A i j.succ = B i j.succ + c j * A i (Fin.castSuccEmb j)) :
+    (A_succ : ∀ (i) (j : Fin n), A i j.succ = B i j.succ + c j * A i (Fin.castSucc j)) :
     det A = det B := by
   rw [← det_transpose A, ← det_transpose B]
   exact det_eq_of_forall_row_eq_smul_add_pred c A_zero fun i j => A_succ j i

c3019c79

chore: rename Fin.castSucc to Fin.castSuccEmb (#5729)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

f4e42872

Diff

@@ -516,7 +516,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const {A B : Matrix n n R} (c : n → R
 theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     ∀ (c : Fin n → R) (_hc : ∀ i : Fin n, k < i.succ → c i = 0)
       {M N : Matrix (Fin n.succ) (Fin n.succ) R} (_h0 : ∀ j, M 0 j = N 0 j)
-      (_hsucc : ∀ (i : Fin n) (j), M i.succ j = N i.succ j + c i * M (Fin.castSucc i) j),
+      (_hsucc : ∀ (i : Fin n) (j), M i.succ j = N i.succ j + c i * M (Fin.castSuccEmb i) j),
       det M = det N := by
   refine' Fin.induction _ (fun k ih => _) k <;> intro c hc M N h0 hsucc
   · congr
@@ -524,16 +524,16 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
     refine' Fin.cases (h0 j) (fun i => _) i
     rw [hsucc, hc i (Fin.succ_pos _), MulZeroClass.zero_mul, add_zero]
   set M' := updateRow M k.succ (N k.succ) with hM'
-  have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSucc k)) := by
+  have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSuccEmb k)) := by
     ext i j
     by_cases hi : i = k.succ
     · simp [hi, hM', hsucc, updateRow_self]
     rw [updateRow_ne hi, hM', updateRow_ne hi]
-  have k_ne_succ : (Fin.castSucc k) ≠ k.succ := (Fin.castSucc_lt_succ k).ne
-  have M_k : M (Fin.castSucc k) = M' (Fin.castSucc k) := (updateRow_ne k_ne_succ).symm
+  have k_ne_succ : (Fin.castSuccEmb k) ≠ k.succ := (Fin.castSuccEmb_lt_succ k).ne
+  have M_k : M (Fin.castSuccEmb k) = M' (Fin.castSuccEmb k) := (updateRow_ne k_ne_succ).symm
   rw [hM, M_k, det_updateRow_add_smul_self M' k_ne_succ.symm, ih (Function.update c k 0)]
   · intro i hi
-    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff] at hi
+    rw [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff] at hi
     rw [Function.update_apply]
     split_ifs with hik
     · rfl
@@ -548,13 +548,13 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
   · simp [hc i (Fin.succ_lt_succ_iff.mpr hik2)]
   rw [updateRow_ne]
   apply ne_of_lt
-  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSucc, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
+  rwa [Fin.lt_iff_val_lt_val, Fin.coe_castSuccEmb, Fin.val_succ, Nat.lt_succ_iff, ← not_lt]
 #align matrix.det_eq_of_forall_row_eq_smul_add_pred_aux Matrix.det_eq_of_forall_row_eq_smul_add_pred_aux
 
 /-- If you add multiples of previous rows to the next row, the determinant doesn't change. -/
 theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ j, A 0 j = B 0 j)
-    (A_succ : ∀ (i : Fin n) (j), A i.succ j = B i.succ j + c i * A (Fin.castSucc i) j) :
+    (A_succ : ∀ (i : Fin n) (j), A i.succ j = B i.succ j + c i * A (Fin.castSuccEmb i) j) :
     det A = det B :=
   det_eq_of_forall_row_eq_smul_add_pred_aux (Fin.last _) c
     (fun _ hi => absurd hi (not_lt_of_ge (Fin.le_last _))) A_zero A_succ
@@ -563,7 +563,7 @@ theorem det_eq_of_forall_row_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n +
 /-- If you add multiples of previous columns to the next columns, the determinant doesn't change. -/
 theorem det_eq_of_forall_col_eq_smul_add_pred {n : ℕ} {A B : Matrix (Fin (n + 1)) (Fin (n + 1)) R}
     (c : Fin n → R) (A_zero : ∀ i, A i 0 = B i 0)
-    (A_succ : ∀ (i) (j : Fin n), A i j.succ = B i j.succ + c j * A i (Fin.castSucc j)) :
+    (A_succ : ∀ (i) (j : Fin n), A i j.succ = B i j.succ + c j * A i (Fin.castSuccEmb j)) :
     det A = det B := by
   rw [← det_transpose A, ← det_transpose B]
   exact det_eq_of_forall_row_eq_smul_add_pred c A_zero fun i j => A_succ j i

c3019c79

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -716,8 +716,7 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   rw [Matrix.det_apply, Finset.univ_perm_fin_succ, ← Finset.univ_product_univ]
   simp only [Finset.sum_map, Equiv.toEmbedding_apply, Finset.sum_product, Matrix.submatrix]
   refine' Finset.sum_congr rfl fun i _ => Fin.cases _ (fun i => _) i
-  ·
-    simp only [Fin.prod_univ_succ, Matrix.det_apply, Finset.mul_sum,
+  · simp only [Fin.prod_univ_succ, Matrix.det_apply, Finset.mul_sum,
       Equiv.Perm.decomposeFin_symm_apply_zero, Fin.val_zero, one_mul,
       Equiv.Perm.decomposeFin.symm_sign, Equiv.swap_self, if_true, id.def, eq_self_iff_true,
       Equiv.Perm.decomposeFin_symm_apply_succ, Fin.succAbove_zero, Equiv.coe_refl, pow_zero,

c3019c79

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -138,7 +138,7 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
     (∑ σ : Perm n, ε σ * ∏ x, M (σ x) (p x) * N (p x) x) = 0 := by
   obtain ⟨i, j, hpij, hij⟩ : ∃ i j, p i = p j ∧ i ≠ j := by
     rw [← Finite.injective_iff_bijective, Injective] at H
-    push_neg  at H
+    push_neg at H
     exact H
   exact
     sum_involution (fun σ _ => σ * Equiv.swap i j)

c3019c79

chore: remove superfluous parentheses in calls to ext (#5258)

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>

3d6731dc

Diff

@@ -481,7 +481,7 @@ theorem det_eq_of_forall_row_eq_smul_add_const_aux {A B : Matrix n n R} {s : Fin
       contrapose! hs
       simp [hs]
     congr
-    ext (i j)
+    ext i j
     rw [A_eq, this, MulZeroClass.zero_mul, add_zero]
   | @insert i s _hi ih =>
     intro c hs k hk A_eq
@@ -520,12 +520,12 @@ theorem det_eq_of_forall_row_eq_smul_add_pred_aux {n : ℕ} (k : Fin (n + 1)) :
       det M = det N := by
   refine' Fin.induction _ (fun k ih => _) k <;> intro c hc M N h0 hsucc
   · congr
-    ext (i j)
+    ext i j
     refine' Fin.cases (h0 j) (fun i => _) i
     rw [hsucc, hc i (Fin.succ_pos _), MulZeroClass.zero_mul, add_zero]
   set M' := updateRow M k.succ (N k.succ) with hM'
   have hM : M = updateRow M' k.succ (M' k.succ + c k • M (Fin.castSucc k)) := by
-    ext (i j)
+    ext i j
     by_cases hi : i = k.succ
     · simp [hi, hM', hsucc, updateRow_self]
     rw [updateRow_ne hi, hM', updateRow_ne hi]
@@ -601,7 +601,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
     simp only [sign_prodCongrLeft, Units.coe_prod, Int.cast_prod, blockDiagonal_apply_eq,
       prodCongrLeft_apply]
   · intro σ σ' _ _ eq
-    ext (x hx k)
+    ext x hx k
     simp only at eq
     have :
       ∀ k x,
@@ -768,7 +768,7 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
   rw [mul_assoc, Matrix.submatrix, Matrix.submatrix]
   congr
   · rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_zero]
-  · ext (i' j')
+  · ext i' j'
     rw [Equiv.Perm.inv_def, Fin.cycleRange_symm_succ]
 #align matrix.det_succ_row Matrix.det_succ_row

c3019c79

chore: minor cleanup after eta's return (#4028)

f44ff708

Diff

@@ -150,7 +150,7 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
       mul_swap_involutive i j σ
 #align matrix.det_mul_aux Matrix.det_mul_aux
 
--- Porting note: need to bump for last simp
+-- Porting note: need to bump for last simp; new after #3414 (reenableeta)
 set_option maxHeartbeats 300000 in
 @[simp]
 theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=

c3019c79

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

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

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

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

a6e1045f

Diff

@@ -59,19 +59,16 @@ variable {R : Type v} [CommRing R]
 -- mathport name: «exprε »
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
-set_option synthInstance.etaExperiment true in
 /-- `det` is an `AlternatingMap` in the rows of the matrix. -/
 def detRowAlternating : AlternatingMap R (n → R) R n :=
   MultilinearMap.alternatization ((MultilinearMap.mkPiAlgebra R n R).compLinearMap LinearMap.proj)
 #align matrix.det_row_alternating Matrix.detRowAlternating
 
-set_option synthInstance.etaExperiment true in
 /-- The determinant of a matrix given by the Leibniz formula. -/
 abbrev det (M : Matrix n n R) : R :=
   detRowAlternating M
 #align matrix.det Matrix.det
 
-set_option synthInstance.etaExperiment true in
 theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, Equiv.Perm.sign σ • ∏ i, M (σ i) i :=
   MultilinearMap.alternatization_apply _ M
 #align matrix.det_apply Matrix.det_apply
@@ -94,7 +91,6 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem det_zero (_ : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
@@ -154,6 +150,8 @@ theorem det_mul_aux {M N : Matrix n n R} {p : n → n} (H : ¬Bijective p) :
       mul_swap_involutive i j σ
 #align matrix.det_mul_aux Matrix.det_mul_aux
 
+-- Porting note: need to bump for last simp
+set_option maxHeartbeats 300000 in
 @[simp]
 theorem det_mul (M N : Matrix n n R) : det (M ⬝ N) = det M * det N :=
   calc
@@ -241,7 +239,6 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det := by
   simp
 #align matrix.det_transpose Matrix.det_transpose
 
-set_option synthInstance.etaExperiment true in
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = Perm.sign σ * M.det :=
@@ -314,7 +311,6 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     _ = (∏ i, v i) * det A := by rw [det_mul, det_diagonal, mul_comm]
 #align matrix.det_mul_row Matrix.det_mul_row
 
-set_option synthInstance.etaExperiment true in
 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_column (v : n → R) (A : Matrix n n R) :
@@ -331,7 +327,6 @@ section HomMap
 
 variable {S : Type w} [CommRing S]
 
-set_option synthInstance.etaExperiment true in
 theorem _root_.RingHom.map_det (f : R →+* S) (M : Matrix n n R) :
     f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]
@@ -354,7 +349,6 @@ theorem _root_.AlgEquiv.map_det [Algebra R S] {T : Type z} [CommRing T] [Algebra
 
 end HomMap
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem det_conjTranspose [StarRing R] (M : Matrix m m R) : det Mᴴ = star (det M) :=
   ((starRingEnd R).map_det _).symm.trans <| congr_arg star M.det_transpose
@@ -369,7 +363,6 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 -/
 
 
-set_option synthInstance.etaExperiment true in
 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
@@ -382,7 +375,6 @@ theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i
 
 variable {M : Matrix n n R} {i j : n}
 
-set_option synthInstance.etaExperiment true in
 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_eq_zero_of_eq M hij i_ne_j
@@ -396,7 +388,6 @@ theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) :
 
 end DetZero
 
-set_option synthInstance.etaExperiment true in
 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_add M j u v
@@ -408,7 +399,6 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
   simp [updateRow_transpose, det_transpose]
 #align matrix.det_update_column_add Matrix.det_updateColumn_add
 
-set_option synthInstance.etaExperiment true in
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_smul M j s u
@@ -420,7 +410,6 @@ theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
   simp [updateRow_transpose, det_transpose]
 #align matrix.det_update_column_smul Matrix.det_updateColumn_smul
 
-set_option synthInstance.etaExperiment true in
 theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateRow M j u) :=
   MultilinearMap.map_update_smul _ M j s u

c3019c79

chore(*): tweak priorities for linear algebra (#3840)

We make sure that the canonical path from NonAssocSemiring to Ring passes through Semiring, as this is a path which is followed all the time in linear algebra where the defining semilinear map σ : R →+* S depends on the NonAssocSemiring structure of R and S while the module definition depends on the Semiring structure.

Tt is not currently possible to adjust priorities by hand (see lean4#2115). Instead, the last declared instance is used, so we make sure that Semiring is declared after NonAssocRing, so that Semiring -> NonAssocSemiring is tried before NonAssocRing -> NonAssocSemiring.

0d22228a

Diff

@@ -331,6 +331,7 @@ section HomMap
 
 variable {S : Type w} [CommRing S]
 
+set_option synthInstance.etaExperiment true in
 theorem _root_.RingHom.map_det (f : R →+* S) (M : Matrix n n R) :
     f M.det = Matrix.det (f.mapMatrix M) :=
   by simp [Matrix.det_apply', f.map_sum, f.map_prod]

c3019c79

chore: bye-bye, solo bys! (#3825)

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".

14167e48

Diff

@@ -126,8 +126,8 @@ theorem det_unique {n : Type _} [Unique n] [DecidableEq n] [Fintype n] (A : Matr
     det A = A default default := by simp [det_apply, univ_unique]
 #align matrix.det_unique Matrix.det_unique
 
-theorem det_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) : det A = A k k :=
-  by
+theorem det_eq_elem_of_subsingleton [Subsingleton n] (A : Matrix n n R) (k : n) :
+    det A = A k k := by
   have := uniqueOfSubsingleton k
   convert det_unique A
 #align matrix.det_eq_elem_of_subsingleton Matrix.det_eq_elem_of_subsingleton
@@ -250,8 +250,8 @@ theorem det_permute (σ : Perm n) (M : Matrix n n R) :
 
 /-- Permuting rows and columns with the same equivalence has no effect. -/
 @[simp]
-theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) : det (A.submatrix e e) = det A :=
-  by
+theorem det_submatrix_equiv_self (e : n ≃ m) (A : Matrix m m R) :
+    det (A.submatrix e e) = det A := by
   rw [det_apply', det_apply']
   apply Fintype.sum_equiv (Equiv.permCongr e)
   intro σ
@@ -373,8 +373,8 @@ theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j
   (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
 
-theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) : det A = 0 :=
-  by
+theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i j = 0) :
+    det A = 0 := by
   rw [← det_transpose]
   exact det_eq_zero_of_row_eq_zero j h
 #align matrix.det_eq_zero_of_column_eq_zero Matrix.det_eq_zero_of_column_eq_zero
@@ -743,16 +743,12 @@ theorem det_succ_column_zero {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R)
   rw [Equiv.Perm.decomposeFin.symm_sign, if_neg (Fin.succ_ne_zero i)]
   calc
     ((-1 * Perm.sign σ : ℤ) • ∏ i', A (Perm.decomposeFin.symm (Fin.succ i, σ) i') i') =
-        (-1 * Perm.sign σ : ℤ) •
-          (A (Fin.succ i) 0 * ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) :=
-      by
+        (-1 * Perm.sign σ : ℤ) • (A (Fin.succ i) 0 *
+          ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) := by
       simp only [Fin.prod_univ_succ, Fin.succAbove_cycleRange,
         Equiv.Perm.decomposeFin_symm_apply_zero, Equiv.Perm.decomposeFin_symm_apply_succ]
-    _ =
-        -1 *
-          (A (Fin.succ i) 0 *
-            (Perm.sign σ : ℤ) •
-              ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) := by
+    _ = -1 * (A (Fin.succ i) 0 * (Perm.sign σ : ℤ) •
+        ∏ i', A ((Fin.succ i).succAbove (Fin.cycleRange i (σ i'))) i'.succ) := by
       simp [mul_assoc, mul_comm, _root_.neg_mul, one_mul, zsmul_eq_mul, neg_inj, neg_smul,
         Fin.succAbove_cycleRange, mul_left_comm]
 #align matrix.det_succ_column_zero Matrix.det_succ_column_zero
@@ -775,7 +771,6 @@ theorem det_succ_row {n : ℕ} (A : Matrix (Fin n.succ) (Fin n.succ) R) (i : Fin
     calc
       det A = ↑((-1 : ℤˣ) ^ (i : ℕ) * (-1 : ℤˣ) ^ (i : ℕ) : ℤˣ) * det A := by simp
       _ = (-1 : R) ^ (i : ℕ) * (Perm.sign i.cycleRange⁻¹) * det A := by simp [-Int.units_mul_self]
-
   rw [this, mul_assoc]
   congr
   rw [← det_permute, det_succ_row_zero]

c3019c79

feat: implement intermediate state for simp_rw (#3738)

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

ff334843

Diff

@@ -588,7 +588,7 @@ theorem det_blockDiagonal {o : Type _} [Fintype o] [DecidableEq o] (M : o → Ma
   simp_rw [det_apply']
   -- The right hand side is a product of sums, rewrite it as a sum of products.
   rw [Finset.prod_sum]
-  simp_rw [Finset.mem_univ, Finset.prod_attach_univ, Finset.univ_pi_univ]
+  simp_rw [Finset.prod_attach_univ, Finset.univ_pi_univ]
   -- We claim that the only permutations contributing to the sum are those that
   -- preserve their second component.
   let preserving_snd : Finset (Equiv.Perm (n × o)) :=

c3019c79

chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

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

0f225a7f

Diff

@@ -59,16 +59,19 @@ variable {R : Type v} [CommRing R]
 -- mathport name: «exprε »
 local notation "ε " σ:arg => ((sign σ : ℤ) : R)
 
+set_option synthInstance.etaExperiment true in
 /-- `det` is an `AlternatingMap` in the rows of the matrix. -/
 def detRowAlternating : AlternatingMap R (n → R) R n :=
   MultilinearMap.alternatization ((MultilinearMap.mkPiAlgebra R n R).compLinearMap LinearMap.proj)
 #align matrix.det_row_alternating Matrix.detRowAlternating
 
+set_option synthInstance.etaExperiment true in
 /-- The determinant of a matrix given by the Leibniz formula. -/
 abbrev det (M : Matrix n n R) : R :=
   detRowAlternating M
 #align matrix.det Matrix.det
 
+set_option synthInstance.etaExperiment true in
 theorem det_apply (M : Matrix n n R) : M.det = ∑ σ : Perm n, Equiv.Perm.sign σ • ∏ i, M (σ i) i :=
   MultilinearMap.alternatization_apply _ M
 #align matrix.det_apply Matrix.det_apply
@@ -91,6 +94,7 @@ theorem det_diagonal {d : n → R} : det (diagonal d) = ∏ i, d i := by
   · simp
 #align matrix.det_diagonal Matrix.det_diagonal
 
+set_option synthInstance.etaExperiment true in
 @[simp]
 theorem det_zero (_ : Nonempty n) : det (0 : Matrix n n R) = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_zero
@@ -237,6 +241,7 @@ theorem det_transpose (M : Matrix n n R) : Mᵀ.det = M.det := by
   simp
 #align matrix.det_transpose Matrix.det_transpose
 
+set_option synthInstance.etaExperiment true in
 /-- Permuting the columns changes the sign of the determinant. -/
 theorem det_permute (σ : Perm n) (M : Matrix n n R) :
     (Matrix.det fun i => M (σ i)) = Perm.sign σ * M.det :=
@@ -309,6 +314,7 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
     _ = (∏ i, v i) * det A := by rw [det_mul, det_diagonal, mul_comm]
 #align matrix.det_mul_row Matrix.det_mul_row
 
+set_option synthInstance.etaExperiment true in
 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
 the product of the `v`s. -/
 theorem det_mul_column (v : n → R) (A : Matrix n n R) :
@@ -362,6 +368,7 @@ Prove that a matrix with a repeated column has determinant equal to zero.
 -/
 
 
+set_option synthInstance.etaExperiment true in
 theorem det_eq_zero_of_row_eq_zero {A : Matrix n n R} (i : n) (h : ∀ j, A i j = 0) : det A = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_coord_zero i (funext h)
 #align matrix.det_eq_zero_of_row_eq_zero Matrix.det_eq_zero_of_row_eq_zero
@@ -374,6 +381,7 @@ theorem det_eq_zero_of_column_eq_zero {A : Matrix n n R} (j : n) (h : ∀ i, A i
 
 variable {M : Matrix n n R} {i j : n}
 
+set_option synthInstance.etaExperiment true in
 /-- If a matrix has a repeated row, the determinant will be zero. -/
 theorem det_zero_of_row_eq (i_ne_j : i ≠ j) (hij : M i = M j) : M.det = 0 :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_eq_zero_of_eq M hij i_ne_j
@@ -387,6 +395,7 @@ theorem det_zero_of_column_eq (i_ne_j : i ≠ j) (hij : ∀ k, M k i = M k j) :
 
 end DetZero
 
+set_option synthInstance.etaExperiment true in
 theorem det_updateRow_add (M : Matrix n n R) (j : n) (u v : n → R) :
     det (updateRow M j <| u + v) = det (updateRow M j u) + det (updateRow M j v) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_add M j u v
@@ -398,6 +407,7 @@ theorem det_updateColumn_add (M : Matrix n n R) (j : n) (u v : n → R) :
   simp [updateRow_transpose, det_transpose]
 #align matrix.det_update_column_add Matrix.det_updateColumn_add
 
+set_option synthInstance.etaExperiment true in
 theorem det_updateRow_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow M j <| s • u) = s * det (updateRow M j u) :=
   (detRowAlternating : AlternatingMap R (n → R) R n).map_smul M j s u
@@ -409,6 +419,7 @@ theorem det_updateColumn_smul (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
   simp [updateRow_transpose, det_transpose]
 #align matrix.det_update_column_smul Matrix.det_updateColumn_smul
 
+set_option synthInstance.etaExperiment true in
 theorem det_updateRow_smul' (M : Matrix n n R) (j : n) (s : R) (u : n → R) :
     det (updateRow (s • M) j u) = s ^ (Fintype.card n - 1) * det (updateRow M j u) :=
   MultilinearMap.map_update_smul _ M j s u

c3019c79

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -279,7 +279,6 @@ theorem det_smul (A : Matrix n n R) (c : R) : det (c • A) = c ^ Fintype.card n
     det (c • A) = det (Matrix.mul (diagonal fun _ => c) A) := by rw [smul_eq_diagonal_mul]
     _ = det (diagonal fun _ => c) * det A := (det_mul _ _)
     _ = c ^ Fintype.card n * det A := by simp [card_univ]
-
 #align matrix.det_smul Matrix.det_smul
 
 @[simp]
@@ -308,7 +307,6 @@ theorem det_mul_row (v : n → R) (A : Matrix n n R) :
         ext
         simp [mul_comm]
     _ = (∏ i, v i) * det A := by rw [det_mul, det_diagonal, mul_comm]
-
 #align matrix.det_mul_row Matrix.det_mul_row
 
 /-- Multiplying each column by a fixed `v j` multiplies the determinant by
@@ -436,7 +434,6 @@ theorem det_eq_of_eq_mul_det_one {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     det A = det (B ⬝ C) := congr_arg _ hA
     _ = det B * det C := (det_mul _ _)
     _ = det B := by rw [hC, mul_one]
-
 #align matrix.det_eq_of_eq_mul_det_one Matrix.det_eq_of_eq_mul_det_one
 
 theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : det C = 1)
@@ -445,7 +442,6 @@ theorem det_eq_of_eq_det_one_mul {A B : Matrix n n R} (C : Matrix n n R) (hC : d
     det A = det (C ⬝ B) := congr_arg _ hA
     _ = det C * det B := (det_mul _ _)
     _ = det B := by rw [hC, one_mul]
-
 #align matrix.det_eq_of_eq_det_one_mul Matrix.det_eq_of_eq_det_one_mul
 
 theorem det_updateRow_add_self (A : Matrix n n R) {i j : n} (hij : i ≠ j) :

c3019c79

feat: port LinearAlgebra.Matrix.Determinant (#3540)

1e61d3d6

`linear_algebra.matrix.determinant` ⟷ `Mathlib.LinearAlgebra.Matrix.Determinant`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 522

linear_algebra.matrix.determinant ⟷ Mathlib.LinearAlgebra.Matrix.Determinant

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 522

`linear_algebra.matrix.determinant` ⟷ `Mathlib.LinearAlgebra.Matrix.Determinant`