linear_algebra.matrix.zpow | 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

03fda911

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f2b757fc

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -129,20 +129,22 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
 -/
 
-#print Matrix.zpow_coe_nat /-
-theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
+/- warning: matrix.zpow_coe_nat clashes with zpow_coe_nat -> zpow_natCast
+Case conversion may be inaccurate. Consider using '#align matrix.zpow_coe_nat zpow_natCastₓ'. -/
+#print zpow_natCast /-
+theorem zpow_natCast (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
   zpow_natCast _ _
-#align matrix.zpow_coe_nat Matrix.zpow_coe_nat
+#align matrix.zpow_coe_nat zpow_natCast
 -/
 
-#print Matrix.zpow_neg_coe_nat /-
+#print Matrix.zpow_neg_natCast /-
 @[simp]
-theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
+theorem zpow_neg_natCast (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   by
   cases n
   · simp
   · exact DivInvMonoid.zpow_neg' _ _
-#align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_nat
+#align matrix.zpow_neg_coe_nat Matrix.zpow_neg_natCast
 -/
 
 #print IsUnit.det_zpow /-
@@ -170,7 +172,7 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
 
 #print Matrix.zpow_neg /-
 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
-  | (n : ℕ) => zpow_neg_coe_nat _ _
+  | (n : ℕ) => zpow_neg_natCast _ _
   | -[n+1] =>
     by
     rw [zpow_negSucc, neg_neg_of_nat_succ, of_nat_eq_coe, zpow_natCast, nonsing_inv_nonsing_inv]

f2b757fc

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -47,7 +47,7 @@ theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   by
   induction' n with n ih
   · simp
-  · rw [pow_succ A, mul_eq_mul, mul_inv_rev, ← ih, ← mul_eq_mul, ← pow_succ']
+  · rw [pow_succ' A, mul_eq_mul, mul_inv_rev, ← ih, ← mul_eq_mul, ← pow_succ]
 #align matrix.inv_pow' Matrix.inv_pow'
 -/
 
@@ -72,11 +72,11 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A
   ·
     calc
       A⁻¹ ^ (m + 1) ⬝ A ^ (n + 1) = A⁻¹ ^ m ⬝ (A⁻¹ ⬝ A) ⬝ A ^ n := by
-        simp only [pow_succ' A⁻¹, pow_succ A, mul_eq_mul, Matrix.mul_assoc]
+        simp only [pow_succ A⁻¹, pow_succ' A, mul_eq_mul, Matrix.mul_assoc]
       _ = A ^ n ⬝ A⁻¹ ^ m := by simp only [h, Matrix.mul_one, Matrix.one_mul, IH m]
       _ = A ^ n ⬝ (A ⬝ A⁻¹) ⬝ A⁻¹ ^ m := by simp only [h', Matrix.mul_one, Matrix.one_mul]
       _ = A ^ (n + 1) ⬝ A⁻¹ ^ (m + 1) := by
-        simp only [pow_succ' A, pow_succ A⁻¹, mul_eq_mul, Matrix.mul_assoc]
+        simp only [pow_succ A, pow_succ' A⁻¹, mul_eq_mul, Matrix.mul_assoc]
   · simp [h]
 #align matrix.pow_inv_comm' Matrix.pow_inv_comm'
 -/
@@ -90,7 +90,7 @@ open Int
 #print Matrix.one_zpow /-
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
-  | (n : ℕ) => by rw [zpow_coe_nat, one_pow]
+  | (n : ℕ) => by rw [zpow_natCast, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
 -/
@@ -98,7 +98,7 @@ theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
 #print Matrix.zero_zpow /-
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
-    rw [zpow_coe_nat, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
+    rw [zpow_natCast, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
     simpa using h
   | -[n+1], h => by simp [zero_pow n.zero_lt_succ]
 #align matrix.zero_zpow Matrix.zero_zpow
@@ -115,7 +115,7 @@ theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
 
 #print Matrix.inv_zpow /-
 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
-  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, inv_pow']
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
 -/
@@ -131,7 +131,7 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
 
 #print Matrix.zpow_coe_nat /-
 theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
-  zpow_coe_nat _ _
+  zpow_natCast _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
 -/
 
@@ -159,7 +159,7 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
   by
   induction' z using Int.induction_on with z IH z IH
   · simp
-  · rw [← Int.ofNat_succ, zpow_coe_nat, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero,
+  · rw [← Int.ofNat_succ, zpow_natCast, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero,
       Int.ofNat_inj]
     simp
   · rw [← neg_add', ← Int.ofNat_succ, zpow_neg_coe_nat, is_unit_nonsing_inv_det_iff, det_pow,
@@ -173,7 +173,7 @@ theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻
   | (n : ℕ) => zpow_neg_coe_nat _ _
   | -[n+1] =>
     by
-    rw [zpow_negSucc, neg_neg_of_nat_succ, of_nat_eq_coe, zpow_coe_nat, nonsing_inv_nonsing_inv]
+    rw [zpow_negSucc, neg_neg_of_nat_succ, of_nat_eq_coe, zpow_natCast, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
@@ -187,15 +187,15 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 
 #print Matrix.zpow_add_one /-
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
-  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_coe_nat]
+  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ, zpow_natCast]
   | -((n : ℕ) + 1) =>
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
-        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_coe_nat]
+        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_natCast]
       _ = (A ⬝ A ^ n)⁻¹ ⬝ A := by
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
-        rw [zpow_neg h, ← Int.ofNat_succ, zpow_coe_nat, pow_succ, mul_eq_mul, mul_eq_mul]
+        rw [zpow_neg h, ← Int.ofNat_succ, zpow_natCast, pow_succ', mul_eq_mul, mul_eq_mul]
 #align matrix.zpow_add_one Matrix.zpow_add_one
 -/
 
@@ -236,7 +236,7 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
   by
   obtain ⟨k, rfl⟩ := eq_coe_of_zero_le hm
   obtain ⟨l, rfl⟩ := eq_coe_of_zero_le hn
-  rw [← Int.ofNat_add, zpow_coe_nat, zpow_coe_nat, zpow_coe_nat, pow_add]
+  rw [← Int.ofNat_add, zpow_natCast, zpow_natCast, zpow_natCast, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
 -/
 
@@ -319,7 +319,7 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
 
 #print Matrix.zpow_add_one_of_ne_neg_one /-
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
-  | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_coe_nat]
+  | (n : ℕ), _ => by simp only [pow_succ, ← Nat.cast_succ, zpow_natCast]
   | -1, h => absurd rfl h
   | -((n : ℕ) + 2), _ =>
     by
@@ -341,16 +341,16 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
 
 #print Matrix.zpow_mul /-
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
-  | (m : ℕ), (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, ← pow_mul, ← zpow_coe_nat, Int.ofNat_mul]
+  | (m : ℕ), (n : ℕ) => by rw [zpow_natCast, zpow_natCast, ← pow_mul, ← zpow_natCast, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
-    rw [zpow_coe_nat, zpow_negSucc, ← pow_mul, coe_nat_mul_neg_succ, ← Int.ofNat_mul,
+    rw [zpow_natCast, zpow_negSucc, ← pow_mul, coe_nat_mul_neg_succ, ← Int.ofNat_mul,
       zpow_neg_coe_nat]
   | -[m+1], (n : ℕ) => by
-    rw [zpow_coe_nat, zpow_negSucc, ← inv_pow', ← pow_mul, neg_succ_mul_coe_nat, ← Int.ofNat_mul,
+    rw [zpow_natCast, zpow_negSucc, ← inv_pow', ← pow_mul, neg_succ_mul_coe_nat, ← Int.ofNat_mul,
       zpow_neg_coe_nat, inv_pow']
   | -[m+1], -[n+1] =>
     by
-    rw [zpow_negSucc, zpow_negSucc, neg_succ_mul_neg_succ, ← Int.ofNat_mul, zpow_coe_nat, inv_pow',
+    rw [zpow_negSucc, zpow_negSucc, neg_succ_mul_neg_succ, ← Int.ofNat_mul, zpow_natCast, inv_pow',
       ← pow_mul, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
@@ -366,7 +366,7 @@ theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n)
 #print Matrix.coe_units_zpow /-
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
-  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_coe_nat, Units.val_pow_eq_pow_val]
+  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_natCast, Units.val_pow_eq_pow_val]
   | -[k+1] => by
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
@@ -428,7 +428,7 @@ theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only
 #print Matrix.transpose_zpow /-
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
-  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, transpose_pow]
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 -/
@@ -436,7 +436,7 @@ theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
 #print Matrix.conjTranspose_zpow /-
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
-  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, conj_transpose_pow]
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, conj_transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, conj_transpose_nonsing_inv, conj_transpose_pow]
 #align matrix.conj_transpose_zpow Matrix.conjTranspose_zpow
 -/

f2b757fc

bump to nightly-2024-02-29-08

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

74acbaea

Diff

@@ -90,7 +90,7 @@ open Int
 #print Matrix.one_zpow /-
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
-  | (n : ℕ) => by rw [zpow_ofNat, one_pow]
+  | (n : ℕ) => by rw [zpow_coe_nat, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
 -/
@@ -98,7 +98,7 @@ theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
 #print Matrix.zero_zpow /-
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
-    rw [zpow_ofNat, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
+    rw [zpow_coe_nat, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
     simpa using h
   | -[n+1], h => by simp [zero_pow n.zero_lt_succ]
 #align matrix.zero_zpow Matrix.zero_zpow
@@ -115,7 +115,7 @@ theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
 
 #print Matrix.inv_zpow /-
 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
-  | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, inv_pow']
+  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
 -/
@@ -131,7 +131,7 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
 
 #print Matrix.zpow_coe_nat /-
 theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
-  zpow_ofNat _ _
+  zpow_coe_nat _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
 -/
 
@@ -159,7 +159,8 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
   by
   induction' z using Int.induction_on with z IH z IH
   · simp
-  · rw [← Int.ofNat_succ, zpow_ofNat, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero, Int.ofNat_inj]
+  · rw [← Int.ofNat_succ, zpow_coe_nat, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero,
+      Int.ofNat_inj]
     simp
   · rw [← neg_add', ← Int.ofNat_succ, zpow_neg_coe_nat, is_unit_nonsing_inv_det_iff, det_pow,
       isUnit_pow_succ_iff, neg_eq_zero, ← Int.ofNat_zero, Int.ofNat_inj]
@@ -172,7 +173,7 @@ theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻
   | (n : ℕ) => zpow_neg_coe_nat _ _
   | -[n+1] =>
     by
-    rw [zpow_negSucc, neg_neg_of_nat_succ, of_nat_eq_coe, zpow_ofNat, nonsing_inv_nonsing_inv]
+    rw [zpow_negSucc, neg_neg_of_nat_succ, of_nat_eq_coe, zpow_coe_nat, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
@@ -186,15 +187,15 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 
 #print Matrix.zpow_add_one /-
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
-  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
+  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_coe_nat]
   | -((n : ℕ) + 1) =>
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
-        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_ofNat]
+        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_coe_nat]
       _ = (A ⬝ A ^ n)⁻¹ ⬝ A := by
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
-        rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ, mul_eq_mul, mul_eq_mul]
+        rw [zpow_neg h, ← Int.ofNat_succ, zpow_coe_nat, pow_succ, mul_eq_mul, mul_eq_mul]
 #align matrix.zpow_add_one Matrix.zpow_add_one
 -/
 
@@ -235,7 +236,7 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
   by
   obtain ⟨k, rfl⟩ := eq_coe_of_zero_le hm
   obtain ⟨l, rfl⟩ := eq_coe_of_zero_le hn
-  rw [← Int.ofNat_add, zpow_ofNat, zpow_ofNat, zpow_ofNat, pow_add]
+  rw [← Int.ofNat_add, zpow_coe_nat, zpow_coe_nat, zpow_coe_nat, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
 -/
 
@@ -318,7 +319,7 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
 
 #print Matrix.zpow_add_one_of_ne_neg_one /-
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
-  | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_ofNat]
+  | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_coe_nat]
   | -1, h => absurd rfl h
   | -((n : ℕ) + 2), _ =>
     by
@@ -340,17 +341,17 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
 
 #print Matrix.zpow_mul /-
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
-  | (m : ℕ), (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]
+  | (m : ℕ), (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, ← pow_mul, ← zpow_coe_nat, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
-    rw [zpow_ofNat, zpow_negSucc, ← pow_mul, coe_nat_mul_neg_succ, ← Int.ofNat_mul,
+    rw [zpow_coe_nat, zpow_negSucc, ← pow_mul, coe_nat_mul_neg_succ, ← Int.ofNat_mul,
       zpow_neg_coe_nat]
   | -[m+1], (n : ℕ) => by
-    rw [zpow_ofNat, zpow_negSucc, ← inv_pow', ← pow_mul, neg_succ_mul_coe_nat, ← Int.ofNat_mul,
+    rw [zpow_coe_nat, zpow_negSucc, ← inv_pow', ← pow_mul, neg_succ_mul_coe_nat, ← Int.ofNat_mul,
       zpow_neg_coe_nat, inv_pow']
   | -[m+1], -[n+1] =>
     by
-    rw [zpow_negSucc, zpow_negSucc, neg_succ_mul_neg_succ, ← Int.ofNat_mul, zpow_ofNat, inv_pow', ←
-      pow_mul, nonsing_inv_nonsing_inv]
+    rw [zpow_negSucc, zpow_negSucc, neg_succ_mul_neg_succ, ← Int.ofNat_mul, zpow_coe_nat, inv_pow',
+      ← pow_mul, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_mul Matrix.zpow_mul
@@ -365,7 +366,7 @@ theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n)
 #print Matrix.coe_units_zpow /-
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
-  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_ofNat, Units.val_pow_eq_pow_val]
+  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_coe_nat, Units.val_pow_eq_pow_val]
   | -[k+1] => by
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
@@ -427,7 +428,7 @@ theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only
 #print Matrix.transpose_zpow /-
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
-  | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, transpose_pow]
+  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 -/
@@ -435,7 +436,7 @@ theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
 #print Matrix.conjTranspose_zpow /-
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
-  | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, conj_transpose_pow]
+  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, conj_transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, conj_transpose_nonsing_inv, conj_transpose_pow]
 #align matrix.conj_transpose_zpow Matrix.conjTranspose_zpow
 -/

f2b757fc

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yakov Pechersky. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
 -/
-import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
+import LinearAlgebra.Matrix.NonsingularInverse
 
 #align_import linear_algebra.matrix.zpow from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"

f2b757fc

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yakov Pechersky. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.zpow
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
 
+#align_import linear_algebra.matrix.zpow from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
 /-!
 # Integer powers of square matrices

f2b757fc

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -37,7 +37,6 @@ namespace Matrix
 
 variable {n' : Type _} [DecidableEq n'] [Fintype n'] {R : Type _} [CommRing R]
 
--- mathport name: exprM
 local notation "M" => Matrix n' n' R
 
 noncomputable instance : DivInvMonoid M :=
@@ -45,6 +44,7 @@ noncomputable instance : DivInvMonoid M :=
 
 section NatPow
 
+#print Matrix.inv_pow' /-
 @[simp]
 theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   by
@@ -52,7 +52,9 @@ theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   · simp
   · rw [pow_succ A, mul_eq_mul, mul_inv_rev, ← ih, ← mul_eq_mul, ← pow_succ']
 #align matrix.inv_pow' Matrix.inv_pow'
+-/
 
+#print Matrix.pow_sub' /-
 theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
     A ^ (m - n) = A ^ m ⬝ (A ^ n)⁻¹ :=
   by
@@ -60,7 +62,9 @@ theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
     tsub_add_cancel_of_le h, Matrix.mul_one]
   simpa using ha.pow n
 #align matrix.pow_sub' Matrix.pow_sub'
+-/
 
+#print Matrix.pow_inv_comm' /-
 theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A⁻¹ ^ m :=
   by
   induction' n with n IH generalizing m
@@ -78,6 +82,7 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A
         simp only [pow_succ' A, pow_succ A⁻¹, mul_eq_mul, Matrix.mul_assoc]
   · simp [h]
 #align matrix.pow_inv_comm' Matrix.pow_inv_comm'
+-/
 
 end NatPow
 
@@ -85,42 +90,55 @@ section Zpow
 
 open Int
 
+#print Matrix.one_zpow /-
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
   | (n : ℕ) => by rw [zpow_ofNat, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
+-/
 
+#print Matrix.zero_zpow /-
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
     rw [zpow_ofNat, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
     simpa using h
   | -[n+1], h => by simp [zero_pow n.zero_lt_succ]
 #align matrix.zero_zpow Matrix.zero_zpow
+-/
 
+#print Matrix.zero_zpow_eq /-
 theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
   by
   split_ifs with h
   · rw [h, zpow_zero]
   · rw [zero_zpow _ h]
 #align matrix.zero_zpow_eq Matrix.zero_zpow_eq
+-/
 
+#print Matrix.inv_zpow /-
 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
+-/
 
+#print Matrix.zpow_neg_one /-
 @[simp]
 theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
   by
   convert DivInvMonoid.zpow_neg' 0 A
   simp only [zpow_one, Int.ofNat_zero, Int.ofNat_succ, zpow_eq_pow, zero_add]
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
+-/
 
+#print Matrix.zpow_coe_nat /-
 theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
   zpow_ofNat _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
+-/
 
+#print Matrix.zpow_neg_coe_nat /-
 @[simp]
 theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   by
@@ -128,14 +146,18 @@ theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   · simp
   · exact DivInvMonoid.zpow_neg' _ _
 #align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_nat
+-/
 
+#print IsUnit.det_zpow /-
 theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).det :=
   by
   cases n
   · simpa using h.pow n
   · simpa using h.pow n.succ
 #align is_unit.det_zpow IsUnit.det_zpow
+-/
 
+#print Matrix.isUnit_det_zpow_iff /-
 theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.det ∨ z = 0 :=
   by
   induction' z using Int.induction_on with z IH z IH
@@ -146,7 +168,9 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
       isUnit_pow_succ_iff, neg_eq_zero, ← Int.ofNat_zero, Int.ofNat_inj]
     simp
 #align matrix.is_unit_det_zpow_iff Matrix.isUnit_det_zpow_iff
+-/
 
+#print Matrix.zpow_neg /-
 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
   | (n : ℕ) => zpow_neg_coe_nat _ _
   | -[n+1] =>
@@ -155,11 +179,15 @@ theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
+-/
 
+#print Matrix.inv_zpow' /-
 theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) := by
   rw [zpow_neg h, inv_zpow]
 #align matrix.inv_zpow' Matrix.inv_zpow'
+-/
 
+#print Matrix.zpow_add_one /-
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
   | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
   | -((n : ℕ) + 1) =>
@@ -171,14 +199,18 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
       _ = A ^ (-(n + 1 : ℤ)) * A := by
         rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ, mul_eq_mul, mul_eq_mul]
 #align matrix.zpow_add_one Matrix.zpow_add_one
+-/
 
+#print Matrix.zpow_sub_one /-
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
   calc
     A ^ (n - 1) = A ^ (n - 1) * A * A⁻¹ := by
       rw [mul_assoc, mul_eq_mul A, mul_nonsing_inv _ h, mul_one]
     _ = A ^ n * A⁻¹ := by rw [← zpow_add_one h, sub_add_cancel]
 #align matrix.zpow_sub_one Matrix.zpow_sub_one
+-/
 
+#print Matrix.zpow_add /-
 theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m * A ^ n :=
   by
   induction' n using Int.induction_on with n ihn n ihn
@@ -186,7 +218,9 @@ theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m *
   · simp only [← add_assoc, zpow_add_one ha, ihn, mul_assoc]
   · rw [zpow_sub_one ha, ← mul_assoc, ← ihn, ← zpow_sub_one ha, add_sub_assoc]
 #align matrix.zpow_add Matrix.zpow_add
+-/
 
+#print Matrix.zpow_add_of_nonpos /-
 theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
     A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -196,7 +230,9 @@ theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
     obtain ⟨l, rfl⟩ := exists_eq_neg_of_nat hn
     simp_rw [← neg_add, ← Int.ofNat_add, zpow_neg_coe_nat, ← inv_pow', h, pow_add]
 #align matrix.zpow_add_of_nonpos Matrix.zpow_add_of_nonpos
+-/
 
+#print Matrix.zpow_add_of_nonneg /-
 theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
     A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -204,11 +240,15 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
   obtain ⟨l, rfl⟩ := eq_coe_of_zero_le hn
   rw [← Int.ofNat_add, zpow_ofNat, zpow_ofNat, zpow_ofNat, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
+-/
 
+#print Matrix.zpow_one_add /-
 theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A ^ i := by
   rw [zpow_add h, zpow_one]
 #align matrix.zpow_one_add Matrix.zpow_one_add
+-/
 
+#print Matrix.SemiconjBy.zpow_right /-
 theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det)
     (h : SemiconjBy A X Y) : ∀ m : ℤ, SemiconjBy A (X ^ m) (Y ^ m)
   | (n : ℕ) => by simp [h.pow_right n]
@@ -227,7 +267,9 @@ theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det
       mul_smul (Y ^ _) (↑hy'.unit⁻¹ : R), mul_adjugate, smul_smul, smul_smul, hx'.coe_inv_mul,
       hy'.coe_inv_mul, one_smul, Matrix.mul_one, Matrix.one_mul]
 #align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_right
+-/
 
+#print Matrix.Commute.zpow_right /-
 theorem Commute.zpow_right {A B : M} (h : Commute A B) (m : ℤ) : Commute A (B ^ m) :=
   by
   rcases nonsing_inv_cancel_or_zero B with (⟨hB, hB'⟩ | hB)
@@ -236,34 +278,48 @@ theorem Commute.zpow_right {A B : M} (h : Commute A B) (m : ℤ) : Commute A (B
     · simpa using h.pow_right _
     · simp [← inv_pow', hB]
 #align matrix.commute.zpow_right Matrix.Commute.zpow_right
+-/
 
+#print Matrix.Commute.zpow_left /-
 theorem Commute.zpow_left {A B : M} (h : Commute A B) (m : ℤ) : Commute (A ^ m) B :=
   (Commute.zpow_right h.symm m).symm
 #align matrix.commute.zpow_left Matrix.Commute.zpow_left
+-/
 
+#print Matrix.Commute.zpow_zpow /-
 theorem Commute.zpow_zpow {A B : M} (h : Commute A B) (m n : ℤ) : Commute (A ^ m) (B ^ n) :=
   Commute.zpow_right (Commute.zpow_left h _) _
 #align matrix.commute.zpow_zpow Matrix.Commute.zpow_zpow
+-/
 
+#print Matrix.Commute.zpow_self /-
 theorem Commute.zpow_self (A : M) (n : ℤ) : Commute (A ^ n) A :=
   Commute.zpow_left (Commute.refl A) _
 #align matrix.commute.zpow_self Matrix.Commute.zpow_self
+-/
 
+#print Matrix.Commute.self_zpow /-
 theorem Commute.self_zpow (A : M) (n : ℤ) : Commute A (A ^ n) :=
   Commute.zpow_right (Commute.refl A) _
 #align matrix.commute.self_zpow Matrix.Commute.self_zpow
+-/
 
+#print Matrix.Commute.zpow_zpow_self /-
 theorem Commute.zpow_zpow_self (A : M) (m n : ℤ) : Commute (A ^ m) (A ^ n) :=
   Commute.zpow_zpow (Commute.refl A) _ _
 #align matrix.commute.zpow_zpow_self Matrix.Commute.zpow_zpow_self
+-/
 
+#print Matrix.zpow_bit0 /-
 theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
   by
   cases' le_total 0 n with nonneg nonpos
   · exact zpow_add_of_nonneg nonneg nonneg
   · exact zpow_add_of_nonpos nonpos nonpos
 #align matrix.zpow_bit0 Matrix.zpow_bit0
+-/
 
+#print Matrix.zpow_add_one_of_ne_neg_one /-
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
   | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_ofNat]
   | -1, h => absurd rfl h
@@ -274,14 +330,18 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
     · show A ^ (-((n + 1 : ℕ) : ℤ)) = A ^ (-((n + 2 : ℕ) : ℤ)) * A
       simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', MulZeroClass.zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
+-/
 
+#print Matrix.zpow_bit1 /-
 theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
   by
   rw [bit1, zpow_add_one_of_ne_neg_one, zpow_bit0]
   intro h
   simpa using congr_arg bodd h
 #align matrix.zpow_bit1 Matrix.zpow_bit1
+-/
 
+#print Matrix.zpow_mul /-
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
   | (m : ℕ), (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
@@ -297,18 +357,24 @@ theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_mul Matrix.zpow_mul
+-/
 
+#print Matrix.zpow_mul' /-
 theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n) ^ m := by
   rw [mul_comm, zpow_mul _ h]
 #align matrix.zpow_mul' Matrix.zpow_mul'
+-/
 
+#print Matrix.coe_units_zpow /-
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
   | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_ofNat, Units.val_pow_eq_pow_val]
   | -[k+1] => by
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
+-/
 
+#print Matrix.zpow_ne_zero_of_isUnit_det /-
 theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : IsUnit A.det)
     (z : ℤ) : A ^ z ≠ 0 := by
   have := ha.det_zpow z
@@ -316,47 +382,66 @@ theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : Is
   rw [this, det_zero ‹_›]
   exact not_isUnit_zero
 #align matrix.zpow_ne_zero_of_is_unit_det Matrix.zpow_ne_zero_of_isUnit_det
+-/
 
+#print Matrix.zpow_sub /-
 theorem zpow_sub {A : M} (ha : IsUnit A.det) (z1 z2 : ℤ) : A ^ (z1 - z2) = A ^ z1 / A ^ z2 := by
   rw [sub_eq_add_neg, zpow_add ha, zpow_neg ha, div_eq_mul_inv]
 #align matrix.zpow_sub Matrix.zpow_sub
+-/
 
+#print Matrix.Commute.mul_zpow /-
 theorem Commute.mul_zpow {A B : M} (h : Commute A B) : ∀ i : ℤ, (A * B) ^ i = A ^ i * B ^ i
   | (n : ℕ) => by simp [h.mul_pow n, -mul_eq_mul]
   | -[n+1] => by
     rw [zpow_negSucc, zpow_negSucc, zpow_negSucc, mul_eq_mul _⁻¹, ← mul_inv_rev, ← mul_eq_mul,
       h.mul_pow n.succ, (h.pow_pow _ _).Eq]
 #align matrix.commute.mul_zpow Matrix.Commute.mul_zpow
+-/
 
+#print Matrix.zpow_bit0' /-
 theorem zpow_bit0' (A : M) (n : ℤ) : A ^ bit0 n = (A * A) ^ n :=
   (zpow_bit0 A n).trans (Commute.mul_zpow (Commute.refl A) n).symm
 #align matrix.zpow_bit0' Matrix.zpow_bit0'
+-/
 
+#print Matrix.zpow_bit1' /-
 theorem zpow_bit1' (A : M) (n : ℤ) : A ^ bit1 n = (A * A) ^ n * A := by
   rw [zpow_bit1, Commute.mul_zpow (Commute.refl A)]
 #align matrix.zpow_bit1' Matrix.zpow_bit1'
+-/
 
+#print Matrix.zpow_neg_mul_zpow_self /-
 theorem zpow_neg_mul_zpow_self (n : ℤ) {A : M} (h : IsUnit A.det) : A ^ (-n) * A ^ n = 1 := by
   rw [zpow_neg h, mul_eq_mul, nonsing_inv_mul _ (h.det_zpow _)]
 #align matrix.zpow_neg_mul_zpow_self Matrix.zpow_neg_mul_zpow_self
+-/
 
+#print Matrix.one_div_pow /-
 theorem one_div_pow {A : M} (n : ℕ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_pow']
 #align matrix.one_div_pow Matrix.one_div_pow
+-/
 
+#print Matrix.one_div_zpow /-
 theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_zpow]
 #align matrix.one_div_zpow Matrix.one_div_zpow
+-/
 
+#print Matrix.transpose_zpow /-
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
+-/
 
+#print Matrix.conjTranspose_zpow /-
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, conj_transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, conj_transpose_nonsing_inv, conj_transpose_pow]
 #align matrix.conj_transpose_zpow Matrix.conjTranspose_zpow
+-/
 
 end Zpow

f2b757fc

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -76,7 +76,6 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A
       _ = A ^ n ⬝ (A ⬝ A⁻¹) ⬝ A⁻¹ ^ m := by simp only [h', Matrix.mul_one, Matrix.one_mul]
       _ = A ^ (n + 1) ⬝ A⁻¹ ^ (m + 1) := by
         simp only [pow_succ' A, pow_succ A⁻¹, mul_eq_mul, Matrix.mul_assoc]
-      
   · simp [h]
 #align matrix.pow_inv_comm' Matrix.pow_inv_comm'
 
@@ -171,7 +170,6 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
         rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ, mul_eq_mul, mul_eq_mul]
-      
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
@@ -179,7 +177,6 @@ theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n
     A ^ (n - 1) = A ^ (n - 1) * A * A⁻¹ := by
       rw [mul_assoc, mul_eq_mul A, mul_nonsing_inv _ h, mul_one]
     _ = A ^ n * A⁻¹ := by rw [← zpow_add_one h, sub_add_cancel]
-    
 #align matrix.zpow_sub_one Matrix.zpow_sub_one
 
 theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m * A ^ n :=

f2b757fc

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -31,7 +31,7 @@ matrix inverse, matrix powers
 -/
 
 
-open Matrix
+open scoped Matrix
 
 namespace Matrix

f2b757fc

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -45,12 +45,6 @@ noncomputable instance : DivInvMonoid M :=
 
 section NatPow
 
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-Case conversion may be inaccurate. Consider using '#align matrix.inv_pow' Matrix.inv_pow'ₓ'. -/
 @[simp]
 theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   by
@@ -59,12 +53,6 @@ theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   · rw [pow_succ A, mul_eq_mul, mul_inv_rev, ← ih, ← mul_eq_mul, ← pow_succ']
 #align matrix.inv_pow' Matrix.inv_pow'
 
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 theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
     A ^ (m - n) = A ^ m ⬝ (A ^ n)⁻¹ :=
   by
@@ -73,12 +61,6 @@ theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
   simpa using ha.pow n
 #align matrix.pow_sub' Matrix.pow_sub'
 
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 theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A⁻¹ ^ m :=
   by
   induction' n with n IH generalizing m
@@ -104,24 +86,12 @@ section Zpow
 
 open Int
 
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 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
   | (n : ℕ) => by rw [zpow_ofNat, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
 
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 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
     rw [zpow_ofNat, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
@@ -129,12 +99,6 @@ theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | -[n+1], h => by simp [zero_pow n.zero_lt_succ]
 #align matrix.zero_zpow Matrix.zero_zpow
 
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 theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
   by
   split_ifs with h
@@ -142,23 +106,11 @@ theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
   · rw [zero_zpow _ h]
 #align matrix.zero_zpow_eq Matrix.zero_zpow_eq
 
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 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
 
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 @[simp]
 theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
   by
@@ -166,22 +118,10 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
   simp only [zpow_one, Int.ofNat_zero, Int.ofNat_succ, zpow_eq_pow, zero_add]
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
 
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 theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
   zpow_ofNat _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
 
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 @[simp]
 theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   by
@@ -190,12 +130,6 @@ theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   · exact DivInvMonoid.zpow_neg' _ _
 #align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_nat
 
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 theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).det :=
   by
   cases n
@@ -203,12 +137,6 @@ theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).de
   · simpa using h.pow n.succ
 #align is_unit.det_zpow IsUnit.det_zpow
 
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 theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.det ∨ z = 0 :=
   by
   induction' z using Int.induction_on with z IH z IH
@@ -220,12 +148,6 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
     simp
 #align matrix.is_unit_det_zpow_iff Matrix.isUnit_det_zpow_iff
 
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 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
   | (n : ℕ) => zpow_neg_coe_nat _ _
   | -[n+1] =>
@@ -235,22 +157,10 @@ theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
 
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 theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) := by
   rw [zpow_neg h, inv_zpow]
 #align matrix.inv_zpow' Matrix.inv_zpow'
 
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 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
   | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
   | -((n : ℕ) + 1) =>
@@ -264,12 +174,6 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
       
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
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 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
   calc
     A ^ (n - 1) = A ^ (n - 1) * A * A⁻¹ := by
@@ -278,12 +182,6 @@ theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n
     
 #align matrix.zpow_sub_one Matrix.zpow_sub_one
 
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 theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m * A ^ n :=
   by
   induction' n using Int.induction_on with n ihn n ihn
@@ -292,12 +190,6 @@ theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m *
   · rw [zpow_sub_one ha, ← mul_assoc, ← ihn, ← zpow_sub_one ha, add_sub_assoc]
 #align matrix.zpow_add Matrix.zpow_add
 
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 theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
     A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -308,12 +200,6 @@ theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
     simp_rw [← neg_add, ← Int.ofNat_add, zpow_neg_coe_nat, ← inv_pow', h, pow_add]
 #align matrix.zpow_add_of_nonpos Matrix.zpow_add_of_nonpos
 
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 theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
     A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -322,22 +208,10 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
   rw [← Int.ofNat_add, zpow_ofNat, zpow_ofNat, zpow_ofNat, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
 
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 theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A ^ i := by
   rw [zpow_add h, zpow_one]
 #align matrix.zpow_one_add Matrix.zpow_one_add
 
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-Case conversion may be inaccurate. Consider using '#align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_rightₓ'. -/
 theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det)
     (h : SemiconjBy A X Y) : ∀ m : ℤ, SemiconjBy A (X ^ m) (Y ^ m)
   | (n : ℕ) => by simp [h.pow_right n]
@@ -357,12 +231,6 @@ theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det
       hy'.coe_inv_mul, one_smul, Matrix.mul_one, Matrix.one_mul]
 #align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_right
 
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 theorem Commute.zpow_right {A B : M} (h : Commute A B) (m : ℤ) : Commute A (B ^ m) :=
   by
   rcases nonsing_inv_cancel_or_zero B with (⟨hB, hB'⟩ | hB)
@@ -372,62 +240,26 @@ theorem Commute.zpow_right {A B : M} (h : Commute A B) (m : ℤ) : Commute A (B
     · simp [← inv_pow', hB]
 #align matrix.commute.zpow_right Matrix.Commute.zpow_right
 
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 theorem Commute.zpow_left {A B : M} (h : Commute A B) (m : ℤ) : Commute (A ^ m) B :=
   (Commute.zpow_right h.symm m).symm
 #align matrix.commute.zpow_left Matrix.Commute.zpow_left
 
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 theorem Commute.zpow_zpow {A B : M} (h : Commute A B) (m n : ℤ) : Commute (A ^ m) (B ^ n) :=
   Commute.zpow_right (Commute.zpow_left h _) _
 #align matrix.commute.zpow_zpow Matrix.Commute.zpow_zpow
 
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 theorem Commute.zpow_self (A : M) (n : ℤ) : Commute (A ^ n) A :=
   Commute.zpow_left (Commute.refl A) _
 #align matrix.commute.zpow_self Matrix.Commute.zpow_self
 
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 theorem Commute.self_zpow (A : M) (n : ℤ) : Commute A (A ^ n) :=
   Commute.zpow_right (Commute.refl A) _
 #align matrix.commute.self_zpow Matrix.Commute.self_zpow
 
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 theorem Commute.zpow_zpow_self (A : M) (m n : ℤ) : Commute (A ^ m) (A ^ n) :=
   Commute.zpow_zpow (Commute.refl A) _ _
 #align matrix.commute.zpow_zpow_self Matrix.Commute.zpow_zpow_self
 
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 theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
   by
   cases' le_total 0 n with nonneg nonpos
@@ -435,12 +267,6 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
   · exact zpow_add_of_nonpos nonpos nonpos
 #align matrix.zpow_bit0 Matrix.zpow_bit0
 
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 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
   | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_ofNat]
   | -1, h => absurd rfl h
@@ -452,12 +278,6 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
       simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', MulZeroClass.zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
 
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 theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
   by
   rw [bit1, zpow_add_one_of_ne_neg_one, zpow_bit0]
@@ -465,12 +285,6 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
   simpa using congr_arg bodd h
 #align matrix.zpow_bit1 Matrix.zpow_bit1
 
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 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
   | (m : ℕ), (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
@@ -487,22 +301,10 @@ theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^
     exact h.pow _
 #align matrix.zpow_mul Matrix.zpow_mul
 
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 theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n) ^ m := by
   rw [mul_comm, zpow_mul _ h]
 #align matrix.zpow_mul' Matrix.zpow_mul'
 
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 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
   | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_ofNat, Units.val_pow_eq_pow_val]
@@ -510,12 +312,6 @@ theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
 
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 theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : IsUnit A.det)
     (z : ℤ) : A ^ z ≠ 0 := by
   have := ha.det_zpow z
@@ -524,22 +320,10 @@ theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : Is
   exact not_isUnit_zero
 #align matrix.zpow_ne_zero_of_is_unit_det Matrix.zpow_ne_zero_of_isUnit_det
 
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 theorem zpow_sub {A : M} (ha : IsUnit A.det) (z1 z2 : ℤ) : A ^ (z1 - z2) = A ^ z1 / A ^ z2 := by
   rw [sub_eq_add_neg, zpow_add ha, zpow_neg ha, div_eq_mul_inv]
 #align matrix.zpow_sub Matrix.zpow_sub
 
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 theorem Commute.mul_zpow {A B : M} (h : Commute A B) : ∀ i : ℤ, (A * B) ^ i = A ^ i * B ^ i
   | (n : ℕ) => by simp [h.mul_pow n, -mul_eq_mul]
   | -[n+1] => by
@@ -547,72 +331,30 @@ theorem Commute.mul_zpow {A B : M} (h : Commute A B) : ∀ i : ℤ, (A * B) ^ i
       h.mul_pow n.succ, (h.pow_pow _ _).Eq]
 #align matrix.commute.mul_zpow Matrix.Commute.mul_zpow
 
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 theorem zpow_bit0' (A : M) (n : ℤ) : A ^ bit0 n = (A * A) ^ n :=
   (zpow_bit0 A n).trans (Commute.mul_zpow (Commute.refl A) n).symm
 #align matrix.zpow_bit0' Matrix.zpow_bit0'
 
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 theorem zpow_bit1' (A : M) (n : ℤ) : A ^ bit1 n = (A * A) ^ n * A := by
   rw [zpow_bit1, Commute.mul_zpow (Commute.refl A)]
 #align matrix.zpow_bit1' Matrix.zpow_bit1'
 
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 theorem zpow_neg_mul_zpow_self (n : ℤ) {A : M} (h : IsUnit A.det) : A ^ (-n) * A ^ n = 1 := by
   rw [zpow_neg h, mul_eq_mul, nonsing_inv_mul _ (h.det_zpow _)]
 #align matrix.zpow_neg_mul_zpow_self Matrix.zpow_neg_mul_zpow_self
 
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 theorem one_div_pow {A : M} (n : ℕ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_pow']
 #align matrix.one_div_pow Matrix.one_div_pow
 
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-Case conversion may be inaccurate. Consider using '#align matrix.one_div_zpow Matrix.one_div_zpowₓ'. -/
 theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_zpow]
 #align matrix.one_div_zpow Matrix.one_div_zpow
 
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-Case conversion may be inaccurate. Consider using '#align matrix.transpose_zpow Matrix.transpose_zpowₓ'. -/
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 
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 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, conj_transpose_pow]

f2b757fc

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -124,8 +124,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align matrix.zero_zpow Matrix.zero_zpowₓ'. -/
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
-    rw [zpow_ofNat, zero_pow]
-    refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
+    rw [zpow_ofNat, zero_pow]; refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
     simpa using h
   | -[n+1], h => by simp [zero_pow n.zero_lt_succ]
 #align matrix.zero_zpow Matrix.zero_zpow

f2b757fc

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -49,7 +49,7 @@ section NatPow
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) (n : Nat), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) n) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) n) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) n) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_pow' Matrix.inv_pow'ₓ'. -/
 @[simp]
 theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
@@ -63,7 +63,7 @@ theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) {m : Nat} {n : Nat}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (LE.le.{0} Nat Nat.hasLe n m) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) m n)) (Matrix.mul.{u2, u1, u1, u1} n' n' n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A m) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n))))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) {m : Nat} {n : Nat}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (LE.le.{0} Nat instLENat n m) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) m n)) (Matrix.mul.{u1, u2, u2, u2} n' n' n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A m) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) {m : Nat} {n : Nat}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (LE.le.{0} Nat instLENat n m) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) m n)) (Matrix.mul.{u1, u2, u2, u2} n' n' n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A m) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))))
 Case conversion may be inaccurate. Consider using '#align matrix.pow_sub' Matrix.pow_sub'ₓ'. -/
 theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
     A ^ (m - n) = A ^ m ⬝ (A ^ n)⁻¹ :=
@@ -77,7 +77,7 @@ theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) (m : Nat) (n : Nat), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (Matrix.mul.{u2, u1, u1, u1} n' n' n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) m) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n)) (Matrix.mul.{u2, u1, u1, u1} n' n' n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) m))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (m : Nat) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (Matrix.mul.{u1, u2, u2, u2} n' n' n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n)) (Matrix.mul.{u1, u2, u2, u2} n' n' n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) m))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (m : Nat) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (Matrix.mul.{u1, u2, u2, u2} n' n' n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n)) (Matrix.mul.{u1, u2, u2, u2} n' n' n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) m))
 Case conversion may be inaccurate. Consider using '#align matrix.pow_inv_comm' Matrix.pow_inv_comm'ₓ'. -/
 theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A⁻¹ ^ m :=
   by
@@ -108,7 +108,7 @@ open Int
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))) n) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3)))))))))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) n) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) n) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align matrix.one_zpow Matrix.one_zpowₓ'. -/
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
@@ -134,7 +134,7 @@ theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 0 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 0 (Zero.zero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasZero.{u2, u1, u1} n' n' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))))))) n) (ite.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (Eq.{1} Int n (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (Int.decidableEq n (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 0 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 0 (Zero.zero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasZero.{u2, u1, u1} n' n' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))))))))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.zero.{u1, u2, u2} n' n' R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) n) (ite.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n' n' R) (Eq.{1} Int n (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Int.instDecidableEqInt n (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.zero.{u1, u2, u2} n' n' R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.zero.{u1, u2, u2} n' n' R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) n) (ite.{succ (max u2 u1)} (Matrix.{u2, u2, u1} n' n' R) (Eq.{1} Int n (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (Int.instDecidableEqInt n (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.zero.{u1, u2, u2} n' n' R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.zero_zpow_eq Matrix.zero_zpow_eqₓ'. -/
 theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
   by
@@ -171,7 +171,7 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) (n : Nat), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n)
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Nat.cast.{0} Int instNatCastInt n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n)
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Nat.cast.{0} Int instNatCastInt n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n)
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_coe_nat Matrix.zpow_coe_natₓ'. -/
 theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
   zpow_ofNat _ _
@@ -181,7 +181,7 @@ theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) (n : Nat), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.hasNeg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Int (HasLiftT.mk.{1, 1} Nat Int (CoeTCₓ.coe.{1, 1} Nat Int (coeBase.{1, 1} Nat Int Int.hasCoe))) n))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt (Nat.cast.{0} Int instNatCastInt n))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_natₓ'. -/
 @[simp]
 theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
@@ -195,7 +195,7 @@ theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
 Case conversion may be inaccurate. Consider using '#align is_unit.det_zpow IsUnit.det_zpowₓ'. -/
 theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).det :=
   by
@@ -208,7 +208,7 @@ theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).de
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} {z : Int}, Iff (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z))) (Or (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) (Eq.{1} Int z (OfNat.ofNat.{0} Int 0 (OfNat.mk.{0} Int 0 (Zero.zero.{0} Int Int.hasZero)))))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {z : Int}, Iff (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z))) (Or (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) (Eq.{1} Int z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {z : Int}, Iff (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z))) (Or (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) (Eq.{1} Int z (OfNat.ofNat.{0} Int 0 (instOfNatInt 0))))
 Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_zpow_iff Matrix.isUnit_det_zpow_iffₓ'. -/
 theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.det ∨ z = 0 :=
   by
@@ -225,7 +225,7 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.hasNeg n)) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt n)) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt n)) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg Matrix.zpow_negₓ'. -/
 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
   | (n : ℕ) => zpow_neg_coe_nat _ _
@@ -240,7 +240,7 @@ theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) n) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.hasNeg n)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) n) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt n)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A) n) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt n)))
 Case conversion may be inaccurate. Consider using '#align matrix.inv_zpow' Matrix.inv_zpow'ₓ'. -/
 theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) := by
   rw [zpow_neg h, inv_zpow]
@@ -250,7 +250,7 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) A))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) A))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) A))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_add_one Matrix.zpow_add_oneₓ'. -/
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
   | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
@@ -269,7 +269,7 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasInv.{u1, u2} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.inv.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) _inst_3) A)))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_sub_one Matrix.zpow_sub_oneₓ'. -/
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
   calc
@@ -283,7 +283,7 @@ theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) m n)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) m n)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) m n)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_add Matrix.zpow_addₓ'. -/
 theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -327,7 +327,7 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (i : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))) i)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) A (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A i)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (i : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) i)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) A (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A i)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (i : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)) i)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) A (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A i)))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_one_add Matrix.zpow_one_addₓ'. -/
 theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A ^ i := by
   rw [zpow_add h, zpow_one]
@@ -337,7 +337,7 @@ theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} {X : Matrix.{u1, u1, u2} n' n' R} {Y : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 X)) -> (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 Y)) -> (SemiconjBy.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) A X Y) -> (forall (m : Int), SemiconjBy.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) A (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) X m) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) Y m))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {X : Matrix.{u2, u2, u1} n' n' R} {Y : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 X)) -> (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 Y)) -> (SemiconjBy.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A X Y) -> (forall (m : Int), SemiconjBy.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) X m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) Y m))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {X : Matrix.{u2, u2, u1} n' n' R} {Y : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 X)) -> (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 Y)) -> (SemiconjBy.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A X Y) -> (forall (m : Int), SemiconjBy.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) X m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) Y m))
 Case conversion may be inaccurate. Consider using '#align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_rightₓ'. -/
 theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det)
     (h : SemiconjBy A X Y) : ∀ m : ℤ, SemiconjBy A (X ^ m) (Y ^ m)
@@ -457,7 +457,7 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (bit1.{0} Int Int.hasOne Int.hasAdd n)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) A)
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) A)
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) A)
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_bit1 Matrix.zpow_bit1ₓ'. -/
 theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
   by
@@ -470,7 +470,7 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R), (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) m n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) n))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) n))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) n))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_mul Matrix.zpow_mulₓ'. -/
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
   | (m : ℕ), (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]
@@ -492,7 +492,7 @@ theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R), (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.hasMul) m n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) m))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) m))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R), (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (m : Int) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HMul.hMul.{0, 0, 0} Int Int Int (instHMul.{0} Int Int.instMulInt) m n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n) m))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_mul' Matrix.zpow_mul'ₓ'. -/
 theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n) ^ m := by
   rw [mul_comm, zpow_mul _ h]
@@ -502,7 +502,7 @@ theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n)
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (u : Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (coeBase.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (Units.hasCoe.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) Int (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (instHPow.{max u1 u2, 0} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) Int (DivInvMonoid.Pow.{max u1 u2} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Group.toDivInvMonoid.{max u1 u2} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Units.group.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))))) u n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) ((fun (a : Type.{max u1 u2}) (b : Type.{max u1 u2}) [self : HasLiftT.{succ (max u1 u2), succ (max u1 u2)} a b] => self.0) (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (coeBase.{succ (max u1 u2), succ (max u1 u2)} (Units.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3)))) (Matrix.{u1, u1, u2} n' n' R) (Units.hasCoe.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))))) u) n)
 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_3 : CommRing.{u2} R] (u : Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (n : Int), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n' n' R) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) Int (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (instHPow.{max u1 u2, 0} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) Int (DivInvMonoid.Pow.{max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (Group.toDivInvMonoid.{max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (Units.instGroupUnits.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))))) u n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.instDivInvMonoidMatrix.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))) u) n)
+  forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (u : Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (n : Int), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n' n' R) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) Int (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (instHPow.{max u1 u2, 0} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) Int (DivInvMonoid.Pow.{max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (Group.toDivInvMonoid.{max u1 u2} (Units.{max u2 u1} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b))))) (Units.instGroupUnits.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))))) u n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.instDivInvMonoidMatrix.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Units.val.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (MonoidWithZero.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Semiring.toMonoidWithZero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.semiring.{u2, u1} n' R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))) u) n)
 Case conversion may be inaccurate. Consider using '#align matrix.coe_units_zpow Matrix.coe_units_zpowₓ'. -/
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
@@ -515,7 +515,7 @@ theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : Nonempty.{succ u1} n'] [_inst_5 : Nontrivial.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (z : Int), Ne.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 0 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 0 (Zero.zero.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasZero.{u2, u1, u1} n' n' R (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))))))))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : Nonempty.{succ u2} n'] [_inst_5 : Nontrivial.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (z : Int), Ne.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.zero.{u1, u2, u2} n' n' R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] [_inst_4 : Nonempty.{succ u2} n'] [_inst_5 : Nontrivial.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (z : Int), Ne.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 0 (Zero.toOfNat0.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.zero.{u1, u2, u2} n' n' R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_ne_zero_of_is_unit_det Matrix.zpow_ne_zero_of_isUnit_detₓ'. -/
 theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : IsUnit A.det)
     (z : ℤ) : A ^ z ≠ 0 := by
@@ -529,7 +529,7 @@ theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : Is
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (z1 : Int) (z2 : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.hasSub) z1 z2)) (HDiv.hDiv.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (DivInvMonoid.toHasDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z1) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z2)))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (z1 : Int) (z2 : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) z1 z2)) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z1) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z2)))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (forall (z1 : Int) (z2 : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (HSub.hSub.{0, 0, 0} Int Int Int (instHSub.{0} Int Int.instSubInt) z1 z2)) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z1) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A z2)))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_sub Matrix.zpow_subₓ'. -/
 theorem zpow_sub {A : M} (ha : IsUnit A.det) (z1 z2 : ℤ) : A ^ (z1 - z2) = A ^ z1 / A ^ z2 := by
   rw [sub_eq_add_neg, zpow_add ha, zpow_neg ha, div_eq_mul_inv]
@@ -562,7 +562,7 @@ theorem zpow_bit0' (A : M) (n : ℤ) : A ^ bit0 n = (A * A) ^ n :=
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} n' n' R) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (bit1.{0} Int Int.hasOne Int.hasAdd n)) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) A A) n) A)
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) A A) n) A)
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} n' n' R) (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) A A) n) A)
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_bit1' Matrix.zpow_bit1'ₓ'. -/
 theorem zpow_bit1' (A : M) (n : ℤ) : A ^ bit1 n = (A * A) ^ n * A := by
   rw [zpow_bit1, Commute.mul_zpow (Commute.refl A)]
@@ -572,7 +572,7 @@ theorem zpow_bit1' (A : M) (n : ℤ) : A ^ bit1 n = (A * A) ^ n * A := by
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] (n : Int) {A : Matrix.{u1, u1, u2} n' n' R}, (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHMul.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.hasNeg n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (n : Int) {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] (n : Int) {A : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 A)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHMul.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A (Neg.neg.{0} Int Int.instNegInt n)) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg_mul_zpow_self Matrix.zpow_neg_mul_zpow_selfₓ'. -/
 theorem zpow_neg_mul_zpow_self (n : ℤ) {A : M} (h : IsUnit A.det) : A ^ (-n) * A ^ n = 1 := by
   rw [zpow_neg h, mul_eq_mul, nonsing_inv_mul _ (h.det_zpow _)]
@@ -582,7 +582,7 @@ theorem zpow_neg_mul_zpow_self (n : ℤ) {A : M} (h : IsUnit A.det) : A ^ (-n) *
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} (n : Nat), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) (HDiv.hDiv.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (DivInvMonoid.toHasDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))) A) n) (HDiv.hDiv.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (DivInvMonoid.toHasDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Nat (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Nat (Monoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Ring.toMonoid.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.ring.{u2, u1} n' R _inst_2 (fun (a : n') (b : n') => _inst_1 a b) (CommRing.toRing.{u2} R _inst_3))))) A n))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A) n) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} (n : Nat), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) A) n) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Nat (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Nat (Monoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (MonoidWithZero.toMonoid.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Semiring.toMonoidWithZero.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.semiring.{u1, u2} n' R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)) _inst_2 (fun (a : n') (b : n') => _inst_1 a b)))))) A n))
 Case conversion may be inaccurate. Consider using '#align matrix.one_div_pow Matrix.one_div_powₓ'. -/
 theorem one_div_pow {A : M} (n : ℕ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_pow']
 #align matrix.one_div_pow Matrix.one_div_pow
@@ -591,7 +591,7 @@ theorem one_div_pow {A : M} (n : ℕ) : (1 / A) ^ n = 1 / A ^ n := by simp only
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HDiv.hDiv.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (DivInvMonoid.toHasDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))) A) n) (HDiv.hDiv.{max u1 u2, max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (Matrix.{u1, u1, u2} n' n' R) (instHDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (DivInvMonoid.toHasDiv.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasOne.{u2, u1} n' R (fun (a : n') (b : n') => _inst_1 a b) (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n))
 but is expected to have type
-  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A) n) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n))
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} (n : Int), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} n' n' R) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) A) n) (HDiv.hDiv.{max u2 u1, max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (Matrix.{u2, u2, u1} n' n' R) (instHDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (DivInvMonoid.toDiv.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.one.{u1, u2} n' R (fun (a : n') (b : n') => _inst_1 a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n))
 Case conversion may be inaccurate. Consider using '#align matrix.one_div_zpow Matrix.one_div_zpowₓ'. -/
 theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_zpow]
 #align matrix.one_div_zpow Matrix.one_div_zpow
@@ -612,7 +612,7 @@ theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
 lean 3 declaration is
   forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : StarRing.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))] (A : Matrix.{u1, u1, u2} n' n' R) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (Matrix.conjTranspose.{u2, u1, u1} n' n' R (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Matrix.conjTranspose.{u2, u1, u1} n' n' R (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) A) n)
 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_3 : CommRing.{u2} R] [_inst_4 : StarRing.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))] (A : Matrix.{u1, u1, u2} n' n' R) (n : Int), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n' n' R) (Matrix.conjTranspose.{u2, u1, u1} n' n' 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_3)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.instDivInvMonoidMatrix.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.instDivInvMonoidMatrix.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Matrix.conjTranspose.{u2, u1, u1} n' n' 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_3)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) A) n)
+  forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))] (A : Matrix.{u1, u1, u2} n' n' R) (n : Int), Eq.{max (succ u1) (succ u2)} (Matrix.{u1, u1, u2} n' n' R) (Matrix.conjTranspose.{u2, u1, u1} n' n' 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_3)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.instDivInvMonoidMatrix.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.instDivInvMonoidMatrix.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Matrix.conjTranspose.{u2, u1, u1} n' n' 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_3)))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) A) n)
 Case conversion may be inaccurate. Consider using '#align matrix.conj_transpose_zpow Matrix.conjTranspose_zpowₓ'. -/
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n

f2b757fc

bump to nightly-2023-04-30-02

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

648ff713

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.zpow
-! leanprover-community/mathlib commit 03fda9112aa6708947da13944a19310684bfdfcb
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
 /-!
 # Integer powers of square matrices
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we define integer power of matrices, relying on
 the nonsingular inverse definition for negative powers.

03fda911

bump to nightly-2023-04-28-12

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

e79952cf

Diff

@@ -42,6 +42,12 @@ noncomputable instance : DivInvMonoid M :=
 
 section NatPow
 
+/- warning: matrix.inv_pow' -> Matrix.inv_pow' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_pow' Matrix.inv_pow'ₓ'. -/
 @[simp]
 theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   by
@@ -50,6 +56,12 @@ theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ :=
   · rw [pow_succ A, mul_eq_mul, mul_inv_rev, ← ih, ← mul_eq_mul, ← pow_succ']
 #align matrix.inv_pow' Matrix.inv_pow'
 
+/- warning: matrix.pow_sub' -> Matrix.pow_sub' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.pow_sub' Matrix.pow_sub'ₓ'. -/
 theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
     A ^ (m - n) = A ^ m ⬝ (A ^ n)⁻¹ :=
   by
@@ -58,6 +70,12 @@ theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
   simpa using ha.pow n
 #align matrix.pow_sub' Matrix.pow_sub'
 
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+Case conversion may be inaccurate. Consider using '#align matrix.pow_inv_comm' Matrix.pow_inv_comm'ₓ'. -/
 theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A⁻¹ ^ m :=
   by
   induction' n with n IH generalizing m
@@ -83,12 +101,24 @@ section Zpow
 
 open Int
 
+/- warning: matrix.one_zpow -> Matrix.one_zpow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.one_zpow Matrix.one_zpowₓ'. -/
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
   | (n : ℕ) => by rw [zpow_ofNat, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zero_zpow Matrix.zero_zpowₓ'. -/
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
     rw [zpow_ofNat, zero_pow]
@@ -97,6 +127,12 @@ theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | -[n+1], h => by simp [zero_pow n.zero_lt_succ]
 #align matrix.zero_zpow Matrix.zero_zpow
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zero_zpow_eq Matrix.zero_zpow_eqₓ'. -/
 theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
   by
   split_ifs with h
@@ -104,11 +140,23 @@ theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 :=
   · rw [zero_zpow _ h]
 #align matrix.zero_zpow_eq Matrix.zero_zpow_eq
 
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_zpow Matrix.inv_zpowₓ'. -/
 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg_one Matrix.zpow_neg_oneₓ'. -/
 @[simp]
 theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
   by
@@ -116,10 +164,22 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ :=
   simp only [zpow_one, Int.ofNat_zero, Int.ofNat_succ, zpow_eq_pow, zero_add]
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_coe_nat Matrix.zpow_coe_natₓ'. -/
 theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
   zpow_ofNat _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_natₓ'. -/
 @[simp]
 theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   by
@@ -128,6 +188,12 @@ theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ :=
   · exact DivInvMonoid.zpow_neg' _ _
 #align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_nat
 
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 theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).det :=
   by
   cases n
@@ -135,6 +201,12 @@ theorem IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).de
   · simpa using h.pow n.succ
 #align is_unit.det_zpow IsUnit.det_zpow
 
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+Case conversion may be inaccurate. Consider using '#align matrix.is_unit_det_zpow_iff Matrix.isUnit_det_zpow_iffₓ'. -/
 theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.det ∨ z = 0 :=
   by
   induction' z using Int.induction_on with z IH z IH
@@ -146,6 +218,12 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
     simp
 #align matrix.is_unit_det_zpow_iff Matrix.isUnit_det_zpow_iff
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg Matrix.zpow_negₓ'. -/
 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
   | (n : ℕ) => zpow_neg_coe_nat _ _
   | -[n+1] =>
@@ -155,10 +233,22 @@ theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
 
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+Case conversion may be inaccurate. Consider using '#align matrix.inv_zpow' Matrix.inv_zpow'ₓ'. -/
 theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) := by
   rw [zpow_neg h, inv_zpow]
 #align matrix.inv_zpow' Matrix.inv_zpow'
 
+/- warning: matrix.zpow_add_one -> Matrix.zpow_add_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_add_one Matrix.zpow_add_oneₓ'. -/
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
   | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
   | -((n : ℕ) + 1) =>
@@ -172,6 +262,12 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
       
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
+/- warning: matrix.zpow_sub_one -> Matrix.zpow_sub_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_sub_one Matrix.zpow_sub_oneₓ'. -/
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
   calc
     A ^ (n - 1) = A ^ (n - 1) * A * A⁻¹ := by
@@ -180,6 +276,12 @@ theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n
     
 #align matrix.zpow_sub_one Matrix.zpow_sub_one
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_add Matrix.zpow_addₓ'. -/
 theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m * A ^ n :=
   by
   induction' n using Int.induction_on with n ihn n ihn
@@ -188,6 +290,12 @@ theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m *
   · rw [zpow_sub_one ha, ← mul_assoc, ← ihn, ← zpow_sub_one ha, add_sub_assoc]
 #align matrix.zpow_add Matrix.zpow_add
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_add_of_nonpos Matrix.zpow_add_of_nonposₓ'. -/
 theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
     A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -198,6 +306,12 @@ theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
     simp_rw [← neg_add, ← Int.ofNat_add, zpow_neg_coe_nat, ← inv_pow', h, pow_add]
 #align matrix.zpow_add_of_nonpos Matrix.zpow_add_of_nonpos
 
+/- warning: matrix.zpow_add_of_nonneg -> Matrix.zpow_add_of_nonneg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonnegₓ'. -/
 theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
     A ^ (m + n) = A ^ m * A ^ n :=
   by
@@ -206,10 +320,22 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
   rw [← Int.ofNat_add, zpow_ofNat, zpow_ofNat, zpow_ofNat, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
 
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 theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A ^ i := by
   rw [zpow_add h, zpow_one]
 #align matrix.zpow_one_add Matrix.zpow_one_add
 
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+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {X : Matrix.{u2, u2, u1} n' n' R} {Y : Matrix.{u2, u2, u1} n' n' R}, (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 X)) -> (IsUnit.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (Matrix.det.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3 Y)) -> (SemiconjBy.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A X Y) -> (forall (m : Int), SemiconjBy.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) X m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) Y m))
+Case conversion may be inaccurate. Consider using '#align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_rightₓ'. -/
 theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det)
     (h : SemiconjBy A X Y) : ∀ m : ℤ, SemiconjBy A (X ^ m) (Y ^ m)
   | (n : ℕ) => by simp [h.pow_right n]
@@ -229,6 +355,12 @@ theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det
       hy'.coe_inv_mul, one_smul, Matrix.mul_one, Matrix.one_mul]
 #align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_right
 
+/- warning: matrix.commute.zpow_right -> Matrix.Commute.zpow_right is a dubious translation:
+lean 3 declaration is
+  forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} {B : Matrix.{u1, u1, u2} n' n' R}, (Commute.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) A B) -> (forall (m : Int), Commute.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) A (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) B m))
+but is expected to have type
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {B : Matrix.{u2, u2, u1} n' n' R}, (Commute.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A B) -> (forall (m : Int), Commute.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) B m))
+Case conversion may be inaccurate. Consider using '#align matrix.commute.zpow_right Matrix.Commute.zpow_rightₓ'. -/
 theorem Commute.zpow_right {A B : M} (h : Commute A B) (m : ℤ) : Commute A (B ^ m) :=
   by
   rcases nonsing_inv_cancel_or_zero B with (⟨hB, hB'⟩ | hB)
@@ -238,26 +370,62 @@ theorem Commute.zpow_right {A B : M} (h : Commute A B) (m : ℤ) : Commute A (B
     · simp [← inv_pow', hB]
 #align matrix.commute.zpow_right Matrix.Commute.zpow_right
 
+/- warning: matrix.commute.zpow_left -> Matrix.Commute.zpow_left is a dubious translation:
+lean 3 declaration is
+  forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} {B : Matrix.{u1, u1, u2} n' n' R}, (Commute.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) A B) -> (forall (m : Int), Commute.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) B)
+but is expected to have type
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {B : Matrix.{u2, u2, u1} n' n' R}, (Commute.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A B) -> (forall (m : Int), Commute.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) B)
+Case conversion may be inaccurate. Consider using '#align matrix.commute.zpow_left Matrix.Commute.zpow_leftₓ'. -/
 theorem Commute.zpow_left {A B : M} (h : Commute A B) (m : ℤ) : Commute (A ^ m) B :=
   (Commute.zpow_right h.symm m).symm
 #align matrix.commute.zpow_left Matrix.Commute.zpow_left
 
+/- warning: matrix.commute.zpow_zpow -> Matrix.Commute.zpow_zpow is a dubious translation:
+lean 3 declaration is
+  forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} n' n' R} {B : Matrix.{u1, u1, u2} n' n' R}, (Commute.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) A B) -> (forall (m : Int) (n : Int), Commute.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.hasMul.{u2, u1} n' R _inst_2 (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3)))))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) B n))
+but is expected to have type
+  forall {n' : Type.{u2}} [_inst_1 : DecidableEq.{succ u2} n'] [_inst_2 : Fintype.{u2} n'] {R : Type.{u1}} [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} n' n' R} {B : Matrix.{u2, u2, u1} n' n' R}, (Commute.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) A B) -> (forall (m : Int) (n : Int), Commute.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instMulMatrix.{u1, u2} n' R _inst_2 (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3)))))) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A m) (HPow.hPow.{max u2 u1, 0, max u2 u1} (Matrix.{u2, u2, u1} n' n' R) Int (Matrix.{u2, u2, u1} n' n' R) (instHPow.{max u2 u1, 0} (Matrix.{u2, u2, u1} n' n' R) Int (DivInvMonoid.Pow.{max u2 u1} (Matrix.{u2, u2, u1} n' n' R) (Matrix.instDivInvMonoidMatrix.{u2, u1} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) B n))
+Case conversion may be inaccurate. Consider using '#align matrix.commute.zpow_zpow Matrix.Commute.zpow_zpowₓ'. -/
 theorem Commute.zpow_zpow {A B : M} (h : Commute A B) (m n : ℤ) : Commute (A ^ m) (B ^ n) :=
   Commute.zpow_right (Commute.zpow_left h _) _
 #align matrix.commute.zpow_zpow Matrix.Commute.zpow_zpow
 
+/- warning: matrix.commute.zpow_self -> Matrix.Commute.zpow_self is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.commute.zpow_self Matrix.Commute.zpow_selfₓ'. -/
 theorem Commute.zpow_self (A : M) (n : ℤ) : Commute (A ^ n) A :=
   Commute.zpow_left (Commute.refl A) _
 #align matrix.commute.zpow_self Matrix.Commute.zpow_self
 
+/- warning: matrix.commute.self_zpow -> Matrix.Commute.self_zpow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.commute.self_zpow Matrix.Commute.self_zpowₓ'. -/
 theorem Commute.self_zpow (A : M) (n : ℤ) : Commute A (A ^ n) :=
   Commute.zpow_right (Commute.refl A) _
 #align matrix.commute.self_zpow Matrix.Commute.self_zpow
 
+/- warning: matrix.commute.zpow_zpow_self -> Matrix.Commute.zpow_zpow_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.commute.zpow_zpow_self Matrix.Commute.zpow_zpow_selfₓ'. -/
 theorem Commute.zpow_zpow_self (A : M) (m n : ℤ) : Commute (A ^ m) (A ^ n) :=
   Commute.zpow_zpow (Commute.refl A) _ _
 #align matrix.commute.zpow_zpow_self Matrix.Commute.zpow_zpow_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_bit0 Matrix.zpow_bit0ₓ'. -/
 theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
   by
   cases' le_total 0 n with nonneg nonpos
@@ -265,6 +433,12 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n :=
   · exact zpow_add_of_nonpos nonpos nonpos
 #align matrix.zpow_bit0 Matrix.zpow_bit0
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_oneₓ'. -/
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
   | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_ofNat]
   | -1, h => absurd rfl h
@@ -276,6 +450,12 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
       simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', MulZeroClass.zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
 
+/- warning: matrix.zpow_bit1 -> Matrix.zpow_bit1 is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_bit1 Matrix.zpow_bit1ₓ'. -/
 theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
   by
   rw [bit1, zpow_add_one_of_ne_neg_one, zpow_bit0]
@@ -283,6 +463,12 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=
   simpa using congr_arg bodd h
 #align matrix.zpow_bit1 Matrix.zpow_bit1
 
+/- warning: matrix.zpow_mul -> Matrix.zpow_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_mul Matrix.zpow_mulₓ'. -/
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
   | (m : ℕ), (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
@@ -299,10 +485,22 @@ theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^
     exact h.pow _
 #align matrix.zpow_mul Matrix.zpow_mul
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_mul' Matrix.zpow_mul'ₓ'. -/
 theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n) ^ m := by
   rw [mul_comm, zpow_mul _ h]
 #align matrix.zpow_mul' Matrix.zpow_mul'
 
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+Case conversion may be inaccurate. Consider using '#align matrix.coe_units_zpow Matrix.coe_units_zpowₓ'. -/
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
   | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_ofNat, Units.val_pow_eq_pow_val]
@@ -310,6 +508,12 @@ theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = u ^ n
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
 
+/- warning: matrix.zpow_ne_zero_of_is_unit_det -> Matrix.zpow_ne_zero_of_isUnit_det is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_ne_zero_of_is_unit_det Matrix.zpow_ne_zero_of_isUnit_detₓ'. -/
 theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : IsUnit A.det)
     (z : ℤ) : A ^ z ≠ 0 := by
   have := ha.det_zpow z
@@ -318,10 +522,22 @@ theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : Is
   exact not_isUnit_zero
 #align matrix.zpow_ne_zero_of_is_unit_det Matrix.zpow_ne_zero_of_isUnit_det
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_sub Matrix.zpow_subₓ'. -/
 theorem zpow_sub {A : M} (ha : IsUnit A.det) (z1 z2 : ℤ) : A ^ (z1 - z2) = A ^ z1 / A ^ z2 := by
   rw [sub_eq_add_neg, zpow_add ha, zpow_neg ha, div_eq_mul_inv]
 #align matrix.zpow_sub Matrix.zpow_sub
 
+/- warning: matrix.commute.mul_zpow -> Matrix.Commute.mul_zpow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.commute.mul_zpow Matrix.Commute.mul_zpowₓ'. -/
 theorem Commute.mul_zpow {A B : M} (h : Commute A B) : ∀ i : ℤ, (A * B) ^ i = A ^ i * B ^ i
   | (n : ℕ) => by simp [h.mul_pow n, -mul_eq_mul]
   | -[n+1] => by
@@ -329,30 +545,72 @@ theorem Commute.mul_zpow {A B : M} (h : Commute A B) : ∀ i : ℤ, (A * B) ^ i
       h.mul_pow n.succ, (h.pow_pow _ _).Eq]
 #align matrix.commute.mul_zpow Matrix.Commute.mul_zpow
 
+/- warning: matrix.zpow_bit0' -> Matrix.zpow_bit0' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_bit0' Matrix.zpow_bit0'ₓ'. -/
 theorem zpow_bit0' (A : M) (n : ℤ) : A ^ bit0 n = (A * A) ^ n :=
   (zpow_bit0 A n).trans (Commute.mul_zpow (Commute.refl A) n).symm
 #align matrix.zpow_bit0' Matrix.zpow_bit0'
 
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_bit1' Matrix.zpow_bit1'ₓ'. -/
 theorem zpow_bit1' (A : M) (n : ℤ) : A ^ bit1 n = (A * A) ^ n * A := by
   rw [zpow_bit1, Commute.mul_zpow (Commute.refl A)]
 #align matrix.zpow_bit1' Matrix.zpow_bit1'
 
+/- warning: matrix.zpow_neg_mul_zpow_self -> Matrix.zpow_neg_mul_zpow_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.zpow_neg_mul_zpow_self Matrix.zpow_neg_mul_zpow_selfₓ'. -/
 theorem zpow_neg_mul_zpow_self (n : ℤ) {A : M} (h : IsUnit A.det) : A ^ (-n) * A ^ n = 1 := by
   rw [zpow_neg h, mul_eq_mul, nonsing_inv_mul _ (h.det_zpow _)]
 #align matrix.zpow_neg_mul_zpow_self Matrix.zpow_neg_mul_zpow_self
 
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+Case conversion may be inaccurate. Consider using '#align matrix.one_div_pow Matrix.one_div_powₓ'. -/
 theorem one_div_pow {A : M} (n : ℕ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_pow']
 #align matrix.one_div_pow Matrix.one_div_pow
 
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+Case conversion may be inaccurate. Consider using '#align matrix.one_div_zpow Matrix.one_div_zpowₓ'. -/
 theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_zpow]
 #align matrix.one_div_zpow Matrix.one_div_zpow
 
+/- warning: matrix.transpose_zpow -> Matrix.transpose_zpow is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.transpose_zpow Matrix.transpose_zpowₓ'. -/
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 
+/- warning: matrix.conj_transpose_zpow -> Matrix.conjTranspose_zpow is a dubious translation:
+lean 3 declaration is
+  forall {n' : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} n'] [_inst_2 : Fintype.{u1} n'] {R : Type.{u2}} [_inst_3 : CommRing.{u2} R] [_inst_4 : StarRing.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))] (A : Matrix.{u1, u1, u2} n' n' R) (n : Int), Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} n' n' R) (Matrix.conjTranspose.{u2, u1, u1} n' n' R (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) A n)) (HPow.hPow.{max u1 u2, 0, max u1 u2} (Matrix.{u1, u1, u2} n' n' R) Int (Matrix.{u1, u1, u2} n' n' R) (instHPow.{max u1 u2, 0} (Matrix.{u1, u1, u2} n' n' R) Int (DivInvMonoid.Pow.{max u1 u2} (Matrix.{u1, u1, u2} n' n' R) (Matrix.divInvMonoid.{u1, u2} n' (fun (a : n') (b : n') => _inst_1 a b) _inst_2 R _inst_3))) (Matrix.conjTranspose.{u2, u1, u1} n' n' R (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3)))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_3))) _inst_4))) A) n)
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+Case conversion may be inaccurate. Consider using '#align matrix.conj_transpose_zpow Matrix.conjTranspose_zpowₓ'. -/
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, conj_transpose_pow]

03fda911

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -273,7 +273,7 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
     rcases nonsing_inv_cancel_or_zero A with (⟨h, h'⟩ | h)
     · apply zpow_add_one (is_unit_det_of_left_inverse h)
     · show A ^ (-((n + 1 : ℕ) : ℤ)) = A ^ (-((n + 2 : ℕ) : ℤ)) * A
-      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', zero_mul]
+      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', MulZeroClass.zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
 
 theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A :=

03fda911

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

03fda911

chore: Rename coe_nat/coe_int/coe_rat to natCast/intCast/ratCast (#11499)

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

b2af0d13

Diff

@@ -107,16 +107,17 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ := by
   simp only [zpow_one, Int.ofNat_zero, Int.ofNat_succ, zpow_eq_pow, zero_add]
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
 
-nonrec theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
-  zpow_natCast _ _
-#align matrix.zpow_coe_nat Matrix.zpow_coe_nat
+#align matrix.zpow_coe_nat zpow_natCast
 
 @[simp]
-theorem zpow_neg_coe_nat (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ := by
+theorem zpow_neg_natCast (A : M) (n : ℕ) : A ^ (-n : ℤ) = (A ^ n)⁻¹ := by
   cases n
   · simp
   · exact DivInvMonoid.zpow_neg' _ _
-#align matrix.zpow_neg_coe_nat Matrix.zpow_neg_coe_nat
+#align matrix.zpow_neg_coe_nat Matrix.zpow_neg_natCast
+
+-- 2024-04-05
+@[deprecated] alias zpow_neg_coe_nat := zpow_neg_natCast
 
 theorem _root_.IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A ^ n).det := by
   cases' n with n n
@@ -127,18 +128,18 @@ theorem _root_.IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A
 theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.det ∨ z = 0 := by
   induction' z using Int.induction_on with z _ z _
   · simp
-  · rw [← Int.ofNat_succ, zpow_coe_nat, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero,
+  · rw [← Int.ofNat_succ, zpow_natCast, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero,
       Int.ofNat_inj]
     simp
-  · rw [← neg_add', ← Int.ofNat_succ, zpow_neg_coe_nat, isUnit_nonsing_inv_det_iff, det_pow,
+  · rw [← neg_add', ← Int.ofNat_succ, zpow_neg_natCast, isUnit_nonsing_inv_det_iff, det_pow,
       isUnit_pow_succ_iff, neg_eq_zero, ← Int.ofNat_zero, Int.ofNat_inj]
     simp
 #align matrix.is_unit_det_zpow_iff Matrix.isUnit_det_zpow_iff
 
 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
-  | (n : ℕ) => zpow_neg_coe_nat _ _
+  | (n : ℕ) => zpow_neg_natCast _ _
   | -[n+1] => by
-    rw [zpow_negSucc, neg_negSucc, zpow_coe_nat, nonsing_inv_nonsing_inv]
+    rw [zpow_negSucc, neg_negSucc, zpow_natCast, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
@@ -148,15 +149,15 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 #align matrix.inv_zpow' Matrix.inv_zpow'
 
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
-  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ, zpow_coe_nat]
+  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ, zpow_natCast]
   | -[n+1] =>
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
-        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_coe_nat]
+        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_natCast]
       _ = (A * A ^ n)⁻¹ * A := by
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
-        rw [zpow_neg h, ← Int.ofNat_succ, zpow_coe_nat, pow_succ']
+        rw [zpow_neg h, ← Int.ofNat_succ, zpow_natCast, pow_succ']
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
@@ -179,14 +180,14 @@ theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
   · exact zpow_add (isUnit_det_of_left_inverse h) m n
   · obtain ⟨k, rfl⟩ := exists_eq_neg_ofNat hm
     obtain ⟨l, rfl⟩ := exists_eq_neg_ofNat hn
-    simp_rw [← neg_add, ← Int.ofNat_add, zpow_neg_coe_nat, ← inv_pow', h, pow_add]
+    simp_rw [← neg_add, ← Int.ofNat_add, zpow_neg_natCast, ← inv_pow', h, pow_add]
 #align matrix.zpow_add_of_nonpos Matrix.zpow_add_of_nonpos
 
 theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
     A ^ (m + n) = A ^ m * A ^ n := by
   obtain ⟨k, rfl⟩ := eq_ofNat_of_zero_le hm
   obtain ⟨l, rfl⟩ := eq_ofNat_of_zero_le hn
-  rw [← Int.ofNat_add, zpow_coe_nat, zpow_coe_nat, zpow_coe_nat, pow_add]
+  rw [← Int.ofNat_add, zpow_natCast, zpow_natCast, zpow_natCast, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
 
 theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A ^ i := by
@@ -248,13 +249,13 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n := by
 #align matrix.zpow_bit0 Matrix.zpow_bit0
 
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
-  | (n : ℕ), _ => by simp only [pow_succ, ← Nat.cast_succ, zpow_coe_nat]
+  | (n : ℕ), _ => by simp only [pow_succ, ← Nat.cast_succ, zpow_natCast]
   | -1, h => absurd rfl h
   | -((n : ℕ) + 2), _ => by
     rcases nonsing_inv_cancel_or_zero A with (⟨h, _⟩ | h)
     · apply zpow_add_one (isUnit_det_of_left_inverse h)
     · show A ^ (-((n + 1 : ℕ) : ℤ)) = A ^ (-((n + 2 : ℕ) : ℤ)) * A
-      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow $ Nat.succ_ne_zero _, zero_mul]
+      simp_rw [zpow_neg_natCast, ← inv_pow', h, zero_pow $ Nat.succ_ne_zero _, zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
 
 set_option linter.deprecated false in
@@ -265,14 +266,14 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A := by
 #align matrix.zpow_bit1 Matrix.zpow_bit1
 
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
-  | (m : ℕ), (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, ← pow_mul, ← zpow_coe_nat, Int.ofNat_mul]
+  | (m : ℕ), (n : ℕ) => by rw [zpow_natCast, zpow_natCast, ← pow_mul, ← zpow_natCast, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
-    rw [zpow_coe_nat, zpow_negSucc, ← pow_mul, ofNat_mul_negSucc, zpow_neg_coe_nat]
+    rw [zpow_natCast, zpow_negSucc, ← pow_mul, ofNat_mul_negSucc, zpow_neg_natCast]
   | -[m+1], (n : ℕ) => by
-    rw [zpow_coe_nat, zpow_negSucc, ← inv_pow', ← pow_mul, negSucc_mul_ofNat, zpow_neg_coe_nat,
+    rw [zpow_natCast, zpow_negSucc, ← inv_pow', ← pow_mul, negSucc_mul_ofNat, zpow_neg_natCast,
         inv_pow']
   | -[m+1], -[n+1] => by
-    rw [zpow_negSucc, zpow_negSucc, negSucc_mul_negSucc, ← Int.ofNat_mul, zpow_coe_nat, inv_pow', ←
+    rw [zpow_negSucc, zpow_negSucc, negSucc_mul_negSucc, ← Int.ofNat_mul, zpow_natCast, inv_pow', ←
       pow_mul, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
@@ -285,7 +286,7 @@ theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n)
 
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = (u : M) ^ n
-  | (n : ℕ) => by rw [zpow_natCast, zpow_coe_nat, Units.val_pow_eq_pow_val]
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, Units.val_pow_eq_pow_val]
   | -[k+1] => by
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
@@ -331,13 +332,13 @@ theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only
 
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
-  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, transpose_pow]
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
-  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, conjTranspose_pow]
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, conjTranspose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, conjTranspose_nonsing_inv, conjTranspose_pow]
 #align matrix.conj_transpose_zpow Matrix.conjTranspose_zpow

03fda911

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

@@ -63,11 +63,11 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m * A ^ n = A ^ n * A⁻¹
   · simp only [Nat.succ_eq_add_one]
     calc
        A⁻¹ ^ (m + 1) * A ^ (n + 1) = A⁻¹ ^ m * (A⁻¹ * A) * A ^ n := by
-        simp only [pow_succ' A⁻¹, pow_succ A, Matrix.mul_assoc]
+        simp only [pow_succ A⁻¹, pow_succ' A, Matrix.mul_assoc]
       _ = A ^ n * A⁻¹ ^ m := by simp only [h, Matrix.mul_one, Matrix.one_mul, IH m]
       _ = A ^ n * (A * A⁻¹) * A⁻¹ ^ m := by simp only [h', Matrix.mul_one, Matrix.one_mul]
       _ = A ^ (n + 1) * A⁻¹ ^ (m + 1) := by
-        simp only [pow_succ' A, pow_succ A⁻¹, Matrix.mul_assoc]
+        simp only [pow_succ A, pow_succ' A⁻¹, Matrix.mul_assoc]
   · simp [h]
 #align matrix.pow_inv_comm' Matrix.pow_inv_comm'
 
@@ -148,7 +148,7 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 #align matrix.inv_zpow' Matrix.inv_zpow'
 
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
-  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_coe_nat]
+  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ, zpow_coe_nat]
   | -[n+1] =>
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
@@ -156,7 +156,7 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
       _ = (A * A ^ n)⁻¹ * A := by
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
-        rw [zpow_neg h, ← Int.ofNat_succ, zpow_coe_nat, pow_succ]
+        rw [zpow_neg h, ← Int.ofNat_succ, zpow_coe_nat, pow_succ']
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
@@ -248,7 +248,7 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n := by
 #align matrix.zpow_bit0 Matrix.zpow_bit0
 
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
-  | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_coe_nat]
+  | (n : ℕ), _ => by simp only [pow_succ, ← Nat.cast_succ, zpow_coe_nat]
   | -1, h => absurd rfl h
   | -((n : ℕ) + 2), _ => by
     rcases nonsing_inv_cancel_or_zero A with (⟨h, _⟩ | h)

03fda911

chore: Rename zpow_coe_nat to zpow_natCast (#11528)

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

75dad162

Diff

@@ -79,13 +79,13 @@ open Int
 
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
-  | (n : ℕ) => by rw [zpow_coe_nat, one_pow]
+  | (n : ℕ) => by rw [zpow_natCast, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
 
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
-    rw [zpow_coe_nat, zero_pow]
+    rw [zpow_natCast, zero_pow]
     exact mod_cast h
   | -[n+1], _ => by simp [zero_pow n.succ_ne_zero]
 #align matrix.zero_zpow Matrix.zero_zpow
@@ -97,7 +97,7 @@ theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 := by
 #align matrix.zero_zpow_eq Matrix.zero_zpow_eq
 
 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
-  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, inv_pow']
+  | (n : ℕ) => by rw [zpow_natCast, zpow_natCast, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
 
@@ -108,7 +108,7 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ := by
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
 
 nonrec theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
-  zpow_coe_nat _ _
+  zpow_natCast _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
 
 @[simp]
@@ -285,7 +285,7 @@ theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n)
 
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = (u : M) ^ n
-  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_coe_nat, Units.val_pow_eq_pow_val]
+  | (n : ℕ) => by rw [zpow_natCast, zpow_coe_nat, Units.val_pow_eq_pow_val]
   | -[k+1] => by
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow

03fda911

fix: correct statement of zpow_ofNat and ofNat_zsmul (#10969)

Previously these were syntactically identical to the corresponding zpow_coe_nat and coe_nat_zsmul lemmas, now they are about OfNat.ofNat.

Unfortunately, almost every call site uses the ofNat name to refer to Nat.cast, so the downstream proofs had to be adjusted too.

d5525380

Diff

@@ -79,13 +79,13 @@ open Int
 
 @[simp]
 theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
-  | (n : ℕ) => by rw [zpow_ofNat, one_pow]
+  | (n : ℕ) => by rw [zpow_coe_nat, one_pow]
   | -[n+1] => by rw [zpow_negSucc, one_pow, inv_one]
 #align matrix.one_zpow Matrix.one_zpow
 
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
-    rw [zpow_ofNat, zero_pow]
+    rw [zpow_coe_nat, zero_pow]
     exact mod_cast h
   | -[n+1], _ => by simp [zero_pow n.succ_ne_zero]
 #align matrix.zero_zpow Matrix.zero_zpow
@@ -97,7 +97,7 @@ theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 := by
 #align matrix.zero_zpow_eq Matrix.zero_zpow_eq
 
 theorem inv_zpow (A : M) : ∀ n : ℤ, A⁻¹ ^ n = (A ^ n)⁻¹
-  | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, inv_pow']
+  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, inv_pow']
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, inv_pow']
 #align matrix.inv_zpow Matrix.inv_zpow
 
@@ -107,8 +107,8 @@ theorem zpow_neg_one (A : M) : A ^ (-1 : ℤ) = A⁻¹ := by
   simp only [zpow_one, Int.ofNat_zero, Int.ofNat_succ, zpow_eq_pow, zero_add]
 #align matrix.zpow_neg_one Matrix.zpow_neg_one
 
-theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
-  zpow_ofNat _ _
+nonrec theorem zpow_coe_nat (A : M) (n : ℕ) : A ^ (n : ℤ) = A ^ n :=
+  zpow_coe_nat _ _
 #align matrix.zpow_coe_nat Matrix.zpow_coe_nat
 
 @[simp]
@@ -127,7 +127,8 @@ theorem _root_.IsUnit.det_zpow {A : M} (h : IsUnit A.det) (n : ℤ) : IsUnit (A
 theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.det ∨ z = 0 := by
   induction' z using Int.induction_on with z _ z _
   · simp
-  · rw [← Int.ofNat_succ, zpow_ofNat, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero, Int.ofNat_inj]
+  · rw [← Int.ofNat_succ, zpow_coe_nat, det_pow, isUnit_pow_succ_iff, ← Int.ofNat_zero,
+      Int.ofNat_inj]
     simp
   · rw [← neg_add', ← Int.ofNat_succ, zpow_neg_coe_nat, isUnit_nonsing_inv_det_iff, det_pow,
       isUnit_pow_succ_iff, neg_eq_zero, ← Int.ofNat_zero, Int.ofNat_inj]
@@ -137,7 +138,7 @@ theorem isUnit_det_zpow_iff {A : M} {z : ℤ} : IsUnit (A ^ z).det ↔ IsUnit A.
 theorem zpow_neg {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (-n) = (A ^ n)⁻¹
   | (n : ℕ) => zpow_neg_coe_nat _ _
   | -[n+1] => by
-    rw [zpow_negSucc, neg_negSucc, zpow_ofNat, nonsing_inv_nonsing_inv]
+    rw [zpow_negSucc, neg_negSucc, zpow_coe_nat, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
 #align matrix.zpow_neg Matrix.zpow_neg
@@ -147,15 +148,15 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 #align matrix.inv_zpow' Matrix.inv_zpow'
 
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
-  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
+  | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_coe_nat]
   | -[n+1] =>
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
-        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_ofNat]
+        rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_coe_nat]
       _ = (A * A ^ n)⁻¹ * A := by
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
-        rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ]
+        rw [zpow_neg h, ← Int.ofNat_succ, zpow_coe_nat, pow_succ]
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
@@ -185,7 +186,7 @@ theorem zpow_add_of_nonneg {A : M} {m n : ℤ} (hm : 0 ≤ m) (hn : 0 ≤ n) :
     A ^ (m + n) = A ^ m * A ^ n := by
   obtain ⟨k, rfl⟩ := eq_ofNat_of_zero_le hm
   obtain ⟨l, rfl⟩ := eq_ofNat_of_zero_le hn
-  rw [← Int.ofNat_add, zpow_ofNat, zpow_ofNat, zpow_ofNat, pow_add]
+  rw [← Int.ofNat_add, zpow_coe_nat, zpow_coe_nat, zpow_coe_nat, pow_add]
 #align matrix.zpow_add_of_nonneg Matrix.zpow_add_of_nonneg
 
 theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A ^ i := by
@@ -247,7 +248,7 @@ theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n := by
 #align matrix.zpow_bit0 Matrix.zpow_bit0
 
 theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n + 1) = A ^ n * A
-  | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_ofNat]
+  | (n : ℕ), _ => by simp only [pow_succ', ← Nat.cast_succ, zpow_coe_nat]
   | -1, h => absurd rfl h
   | -((n : ℕ) + 2), _ => by
     rcases nonsing_inv_cancel_or_zero A with (⟨h, _⟩ | h)
@@ -264,14 +265,14 @@ theorem zpow_bit1 (A : M) (n : ℤ) : A ^ bit1 n = A ^ n * A ^ n * A := by
 #align matrix.zpow_bit1 Matrix.zpow_bit1
 
 theorem zpow_mul (A : M) (h : IsUnit A.det) : ∀ m n : ℤ, A ^ (m * n) = (A ^ m) ^ n
-  | (m : ℕ), (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]
+  | (m : ℕ), (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, ← pow_mul, ← zpow_coe_nat, Int.ofNat_mul]
   | (m : ℕ), -[n+1] => by
-    rw [zpow_ofNat, zpow_negSucc, ← pow_mul, ofNat_mul_negSucc, zpow_neg_coe_nat]
+    rw [zpow_coe_nat, zpow_negSucc, ← pow_mul, ofNat_mul_negSucc, zpow_neg_coe_nat]
   | -[m+1], (n : ℕ) => by
-    rw [zpow_ofNat, zpow_negSucc, ← inv_pow', ← pow_mul, negSucc_mul_ofNat, zpow_neg_coe_nat,
+    rw [zpow_coe_nat, zpow_negSucc, ← inv_pow', ← pow_mul, negSucc_mul_ofNat, zpow_neg_coe_nat,
         inv_pow']
   | -[m+1], -[n+1] => by
-    rw [zpow_negSucc, zpow_negSucc, negSucc_mul_negSucc, ← Int.ofNat_mul, zpow_ofNat, inv_pow', ←
+    rw [zpow_negSucc, zpow_negSucc, negSucc_mul_negSucc, ← Int.ofNat_mul, zpow_coe_nat, inv_pow', ←
       pow_mul, nonsing_inv_nonsing_inv]
     rw [det_pow]
     exact h.pow _
@@ -284,7 +285,7 @@ theorem zpow_mul' (A : M) (h : IsUnit A.det) (m n : ℤ) : A ^ (m * n) = (A ^ n)
 
 @[simp, norm_cast]
 theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = (u : M) ^ n
-  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_ofNat, Units.val_pow_eq_pow_val]
+  | (n : ℕ) => by rw [_root_.zpow_coe_nat, zpow_coe_nat, Units.val_pow_eq_pow_val]
   | -[k+1] => by
     rw [zpow_negSucc, zpow_negSucc, ← inv_pow, u⁻¹.val_pow_eq_pow_val, ← inv_pow', coe_units_inv]
 #align matrix.coe_units_zpow Matrix.coe_units_zpow
@@ -330,13 +331,13 @@ theorem one_div_zpow {A : M} (n : ℤ) : (1 / A) ^ n = 1 / A ^ n := by simp only
 
 @[simp]
 theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
-  | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, transpose_pow]
+  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, transpose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
-  | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, conjTranspose_pow]
+  | (n : ℕ) => by rw [zpow_coe_nat, zpow_coe_nat, conjTranspose_pow]
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, conjTranspose_nonsing_inv, conjTranspose_pow]
 #align matrix.conj_transpose_zpow Matrix.conjTranspose_zpow

03fda911

feat: The support of f ^ n (#9617)

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

9d1a7d26

Diff

@@ -86,9 +86,8 @@ theorem one_zpow : ∀ n : ℤ, (1 : M) ^ n = 1
 theorem zero_zpow : ∀ z : ℤ, z ≠ 0 → (0 : M) ^ z = 0
   | (n : ℕ), h => by
     rw [zpow_ofNat, zero_pow]
-    refine' lt_of_le_of_ne n.zero_le (Ne.symm _)
-    simpa using h
-  | -[n+1], _ => by simp [zero_pow n.zero_lt_succ]
+    exact mod_cast h
+  | -[n+1], _ => by simp [zero_pow n.succ_ne_zero]
 #align matrix.zero_zpow Matrix.zero_zpow
 
 theorem zero_zpow_eq (n : ℤ) : (0 : M) ^ n = if n = 0 then 1 else 0 := by
@@ -254,7 +253,7 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
     rcases nonsing_inv_cancel_or_zero A with (⟨h, _⟩ | h)
     · apply zpow_add_one (isUnit_det_of_left_inverse h)
     · show A ^ (-((n + 1 : ℕ) : ℤ)) = A ^ (-((n + 2 : ℕ) : ℤ)) * A
-      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', zero_mul]
+      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow $ Nat.succ_ne_zero _, zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
 
 set_option linter.deprecated false in

03fda911

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -242,7 +242,7 @@ theorem Commute.zpow_zpow_self (A : M) (m n : ℤ) : Commute (A ^ m) (A ^ n) :=
 
 set_option linter.deprecated false in
 theorem zpow_bit0 (A : M) (n : ℤ) : A ^ bit0 n = A ^ n * A ^ n := by
-  cases' le_total 0 n with nonneg nonpos
+  rcases le_total 0 n with nonneg | nonpos
   · exact zpow_add_of_nonneg nonneg nonneg
   · exact zpow_add_of_nonpos nonpos nonpos
 #align matrix.zpow_bit0 Matrix.zpow_bit0

03fda911

feat(LinearAlgebra/Matrix): powers preserve IsSymm and IsHermitian (#9036)

120efa76

Diff

@@ -3,8 +3,9 @@ Copyright (c) 2021 Yakov Pechersky. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
 -/
-import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
 import Mathlib.Data.Int.Bitwise
+import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
+import Mathlib.LinearAlgebra.Matrix.Symmetric
 
 #align_import linear_algebra.matrix.zpow from "leanprover-community/mathlib"@"03fda9112aa6708947da13944a19310684bfdfcb"
 
@@ -340,6 +341,10 @@ theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, conjTranspose_nonsing_inv, conjTranspose_pow]
 #align matrix.conj_transpose_zpow Matrix.conjTranspose_zpow
 
+theorem IsSymm.zpow {A : M} (h : A.IsSymm) (k : ℤ) :
+    (A ^ k).IsSymm := by
+  rw [IsSymm, transpose_zpow, h]
+
 end ZPow
 
 end Matrix

03fda911

chore: reduce imports to Data.Rat.Cast.CharZero (#7091)

Removing further unnecessary imports on the path to major tactics.

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

9893bbd2

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
 -/
 import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
+import Mathlib.Data.Int.Bitwise
 
 #align_import linear_algebra.matrix.zpow from "leanprover-community/mathlib"@"03fda9112aa6708947da13944a19310684bfdfcb"
 
@@ -17,7 +18,7 @@ the nonsingular inverse definition for negative powers.
 
 The main definition is a direct recursive call on the integer inductive type,
 as provided by the `DivInvMonoid.Pow` default implementation.
-The lemma names are taken from `Algebra.group_with_zero.power`.
+The lemma names are taken from `Algebra.GroupWithZero.Power`.
 
 ## Tags

03fda911

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

@@ -252,7 +252,7 @@ theorem zpow_add_one_of_ne_neg_one {A : M} : ∀ n : ℤ, n ≠ -1 → A ^ (n +
     rcases nonsing_inv_cancel_or_zero A with (⟨h, _⟩ | h)
     · apply zpow_add_one (isUnit_det_of_left_inverse h)
     · show A ^ (-((n + 1 : ℕ) : ℤ)) = A ^ (-((n + 2 : ℕ) : ℤ)) * A
-      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', MulZeroClass.zero_mul]
+      simp_rw [zpow_neg_coe_nat, ← inv_pow', h, zero_pow Nat.succ_pos', zero_mul]
 #align matrix.zpow_add_one_of_ne_neg_one Matrix.zpow_add_one_of_ne_neg_one
 
 set_option linter.deprecated false in

03fda911

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

@@ -42,17 +42,17 @@ section NatPow
 theorem inv_pow' (A : M) (n : ℕ) : A⁻¹ ^ n = (A ^ n)⁻¹ := by
   induction' n with n ih
   · simp
-  · rw [pow_succ A, mul_eq_mul, mul_inv_rev, ← ih, ← mul_eq_mul, ← pow_succ']
+  · rw [pow_succ A, mul_inv_rev, ← ih, ← pow_succ']
 #align matrix.inv_pow' Matrix.inv_pow'
 
 theorem pow_sub' (A : M) {m n : ℕ} (ha : IsUnit A.det) (h : n ≤ m) :
-    A ^ (m - n) = A ^ m ⬝ (A ^ n)⁻¹ := by
-  rw [← tsub_add_cancel_of_le h, pow_add, mul_eq_mul, Matrix.mul_assoc, mul_nonsing_inv,
+    A ^ (m - n) = A ^ m * (A ^ n)⁻¹ := by
+  rw [← tsub_add_cancel_of_le h, pow_add, Matrix.mul_assoc, mul_nonsing_inv,
     tsub_add_cancel_of_le h, Matrix.mul_one]
   simpa using ha.pow n
 #align matrix.pow_sub' Matrix.pow_sub'
 
-theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A⁻¹ ^ m := by
+theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m * A ^ n = A ^ n * A⁻¹ ^ m := by
   induction' n with n IH generalizing m
   · simp
   cases' m with m m
@@ -60,12 +60,12 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A
   rcases nonsing_inv_cancel_or_zero A with (⟨h, h'⟩ | h)
   · simp only [Nat.succ_eq_add_one]
     calc
-       A⁻¹ ^ (m + 1) ⬝ A ^ (n + 1) = A⁻¹ ^ m ⬝ (A⁻¹ ⬝ A) ⬝ A ^ n := by
-        simp only [pow_succ' A⁻¹, pow_succ A, mul_eq_mul, Matrix.mul_assoc]
-      _ = A ^ n ⬝ A⁻¹ ^ m := by simp only [h, Matrix.mul_one, Matrix.one_mul, IH m]
-      _ = A ^ n ⬝ (A ⬝ A⁻¹) ⬝ A⁻¹ ^ m := by simp only [h', Matrix.mul_one, Matrix.one_mul]
-      _ = A ^ (n + 1) ⬝ A⁻¹ ^ (m + 1) := by
-        simp only [pow_succ' A, pow_succ A⁻¹, mul_eq_mul, Matrix.mul_assoc]
+       A⁻¹ ^ (m + 1) * A ^ (n + 1) = A⁻¹ ^ m * (A⁻¹ * A) * A ^ n := by
+        simp only [pow_succ' A⁻¹, pow_succ A, Matrix.mul_assoc]
+      _ = A ^ n * A⁻¹ ^ m := by simp only [h, Matrix.mul_one, Matrix.one_mul, IH m]
+      _ = A ^ n * (A * A⁻¹) * A⁻¹ ^ m := by simp only [h', Matrix.mul_one, Matrix.one_mul]
+      _ = A ^ (n + 1) * A⁻¹ ^ (m + 1) := by
+        simp only [pow_succ' A, pow_succ A⁻¹, Matrix.mul_assoc]
   · simp [h]
 #align matrix.pow_inv_comm' Matrix.pow_inv_comm'
 
@@ -151,16 +151,16 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
         rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_ofNat]
-      _ = (A ⬝ A ^ n)⁻¹ ⬝ A := by
+      _ = (A * A ^ n)⁻¹ * A := by
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
-        rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ, mul_eq_mul, mul_eq_mul]
+        rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ]
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
   calc
     A ^ (n - 1) = A ^ (n - 1) * A * A⁻¹ := by
-      rw [mul_assoc, mul_eq_mul A, mul_nonsing_inv _ h, mul_one]
+      rw [mul_assoc, mul_nonsing_inv _ h, mul_one]
     _ = A ^ n * A⁻¹ := by rw [← zpow_add_one h, sub_add_cancel]
 #align matrix.zpow_sub_one Matrix.zpow_sub_one
 
@@ -204,8 +204,8 @@ theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det
     rw [zpow_negSucc, zpow_negSucc, nonsing_inv_apply _ hx', nonsing_inv_apply _ hy', SemiconjBy]
     refine' (isRegular_of_isLeftRegular_det hy'.isRegular.left).left _
     dsimp only
-    rw [← mul_assoc, ← (h.pow_right n.succ).eq, mul_assoc, mul_eq_mul (X ^ _), mul_smul,
-      mul_adjugate, mul_eq_mul, mul_eq_mul, mul_eq_mul, ← Matrix.mul_assoc,
+    rw [← mul_assoc, ← (h.pow_right n.succ).eq, mul_assoc, mul_smul,
+      mul_adjugate, ← Matrix.mul_assoc,
       mul_smul (Y ^ _) (↑hy'.unit⁻¹ : R), mul_adjugate, smul_smul, smul_smul, hx'.val_inv_mul,
       hy'.val_inv_mul, one_smul, Matrix.mul_one, Matrix.one_mul]
 #align matrix.semiconj_by.zpow_right Matrix.SemiconjBy.zpow_right
@@ -301,9 +301,9 @@ theorem zpow_sub {A : M} (ha : IsUnit A.det) (z1 z2 : ℤ) : A ^ (z1 - z2) = A ^
 #align matrix.zpow_sub Matrix.zpow_sub
 
 theorem Commute.mul_zpow {A B : M} (h : Commute A B) : ∀ i : ℤ, (A * B) ^ i = A ^ i * B ^ i
-  | (n : ℕ) => by simp [h.mul_pow n, -mul_eq_mul]
+  | (n : ℕ) => by simp [h.mul_pow n]
   | -[n+1] => by
-    rw [zpow_negSucc, zpow_negSucc, zpow_negSucc, mul_eq_mul _⁻¹, ← mul_inv_rev, ← mul_eq_mul,
+    rw [zpow_negSucc, zpow_negSucc, zpow_negSucc, ← mul_inv_rev,
       h.mul_pow n.succ, (h.pow_pow _ _).eq]
 #align matrix.commute.mul_zpow Matrix.Commute.mul_zpow
 
@@ -318,7 +318,7 @@ theorem zpow_bit1' (A : M) (n : ℤ) : A ^ bit1 n = (A * A) ^ n * A := by
 #align matrix.zpow_bit1' Matrix.zpow_bit1'
 
 theorem zpow_neg_mul_zpow_self (n : ℤ) {A : M} (h : IsUnit A.det) : A ^ (-n) * A ^ n = 1 := by
-  rw [zpow_neg h, mul_eq_mul, nonsing_inv_mul _ (h.det_zpow _)]
+  rw [zpow_neg h, nonsing_inv_mul _ (h.det_zpow _)]
 #align matrix.zpow_neg_mul_zpow_self Matrix.zpow_neg_mul_zpow_self
 
 theorem one_div_pow {A : M} (n : ℕ) : (1 / A) ^ n = 1 / A ^ n := by simp only [one_div, inv_pow']

03fda911

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

@@ -29,7 +29,7 @@ open Matrix
 
 namespace Matrix
 
-variable {n' : Type _} [DecidableEq n'] [Fintype n'] {R : Type _} [CommRing R]
+variable {n' : Type*} [DecidableEq n'] [Fintype n'] {R : Type*} [CommRing R]
 
 local notation "M" => Matrix n' n' R

03fda911

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yakov Pechersky. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.zpow
-! leanprover-community/mathlib commit 03fda9112aa6708947da13944a19310684bfdfcb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
 
+#align_import linear_algebra.matrix.zpow from "leanprover-community/mathlib"@"03fda9112aa6708947da13944a19310684bfdfcb"
+
 /-!
 # Integer powers of square matrices

03fda911

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

@@ -61,8 +61,8 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A
   cases' m with m m
   · simp
   rcases nonsing_inv_cancel_or_zero A with (⟨h, h'⟩ | h)
-  ·  simp only [Nat.succ_eq_add_one]
-     calc
+  · simp only [Nat.succ_eq_add_one]
+    calc
        A⁻¹ ^ (m + 1) ⬝ A ^ (n + 1) = A⁻¹ ^ m ⬝ (A⁻¹ ⬝ A) ⬝ A ^ n := by
         simp only [pow_succ' A⁻¹, pow_succ A, mul_eq_mul, Matrix.mul_assoc]
       _ = A ^ n ⬝ A⁻¹ ^ m := by simp only [h, Matrix.mul_one, Matrix.one_mul, IH m]

03fda911

fix(Tactic/PushNeg): add cleanupAnnotations to push_neg (#5082)

Exprs now have an mdata field. It seems that this gets in the way of push_neg, as reported on Zulip.

The above seems to fix the reported errors.

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

868e361b

Diff

@@ -294,11 +294,7 @@ theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = (u : M) ^
 theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : IsUnit A.det)
     (z : ℤ) : A ^ z ≠ 0 := by
   have := ha.det_zpow z
-  -- Porting note: was `contrapose! this`
-  revert this
-  contrapose!
-  rw [ne_eq, not_not]
-  intro this
+  contrapose! this
   rw [this, det_zero ‹_›]
   exact not_isUnit_zero
 #align matrix.zpow_ne_zero_of_is_unit_det Matrix.zpow_ne_zero_of_isUnit_det

03fda911

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

@@ -194,8 +194,6 @@ theorem zpow_one_add {A : M} (h : IsUnit A.det) (i : ℤ) : A ^ (1 + i) = A * A
   rw [zpow_add h, zpow_one]
 #align matrix.zpow_one_add Matrix.zpow_one_add
 
--- porting note: without etaExperiment it failes to synthesize DistribMulAction Rˣ R
-set_option synthInstance.etaExperiment true in
 theorem SemiconjBy.zpow_right {A X Y : M} (hx : IsUnit X.det) (hy : IsUnit Y.det)
     (h : SemiconjBy A X Y) : ∀ m : ℤ, SemiconjBy A (X ^ m) (Y ^ m)
   | (n : ℕ) => by simp [h.pow_right n]
@@ -342,8 +340,6 @@ theorem transpose_zpow (A : M) : ∀ n : ℤ, (A ^ n)ᵀ = Aᵀ ^ n
   | -[n+1] => by rw [zpow_negSucc, zpow_negSucc, transpose_nonsing_inv, transpose_pow]
 #align matrix.transpose_zpow Matrix.transpose_zpow
 
--- porting note: without etaExperiment, conjTranspose_pow can't find the StarRing R instance.
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem conjTranspose_zpow [StarRing R] (A : M) : ∀ n : ℤ, (A ^ n)ᴴ = Aᴴ ^ n
   | (n : ℕ) => by rw [zpow_ofNat, zpow_ofNat, conjTranspose_pow]

03fda911

chore: tidy various files (#3718)

2215ff4f

Diff

@@ -34,7 +34,6 @@ namespace Matrix
 
 variable {n' : Type _} [DecidableEq n'] [Fintype n'] {R : Type _} [CommRing R]
 
--- mathport name: exprM
 local notation "M" => Matrix n' n' R
 
 noncomputable instance : DivInvMonoid M :=
@@ -70,7 +69,6 @@ theorem pow_inv_comm' (A : M) (m n : ℕ) : A⁻¹ ^ m ⬝ A ^ n = A ^ n ⬝ A
       _ = A ^ n ⬝ (A ⬝ A⁻¹) ⬝ A⁻¹ ^ m := by simp only [h', Matrix.mul_one, Matrix.one_mul]
       _ = A ^ (n + 1) ⬝ A⁻¹ ^ (m + 1) := by
         simp only [pow_succ' A, pow_succ A⁻¹, mul_eq_mul, Matrix.mul_assoc]
-
   · simp [h]
 #align matrix.pow_inv_comm' Matrix.pow_inv_comm'
 
@@ -152,7 +150,7 @@ theorem inv_zpow' {A : M} (h : IsUnit A.det) (n : ℤ) : A⁻¹ ^ n = A ^ (-n) :
 
 theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^ n * A
   | (n : ℕ) => by simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]
-  | -((n : ℕ) + 1) =>
+  | -[n+1] =>
     calc
       A ^ (-(n + 1) + 1 : ℤ) = (A ^ n)⁻¹ := by
         rw [neg_add, neg_add_cancel_right, zpow_neg h, zpow_ofNat]
@@ -160,7 +158,6 @@ theorem zpow_add_one {A : M} (h : IsUnit A.det) : ∀ n : ℤ, A ^ (n + 1) = A ^
         rw [mul_inv_rev, Matrix.mul_assoc, nonsing_inv_mul _ h, Matrix.mul_one]
       _ = A ^ (-(n + 1 : ℤ)) * A := by
         rw [zpow_neg h, ← Int.ofNat_succ, zpow_ofNat, pow_succ, mul_eq_mul, mul_eq_mul]
-
 #align matrix.zpow_add_one Matrix.zpow_add_one
 
 theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n * A⁻¹ :=
@@ -168,14 +165,13 @@ theorem zpow_sub_one {A : M} (h : IsUnit A.det) (n : ℤ) : A ^ (n - 1) = A ^ n
     A ^ (n - 1) = A ^ (n - 1) * A * A⁻¹ := by
       rw [mul_assoc, mul_eq_mul A, mul_nonsing_inv _ h, mul_one]
     _ = A ^ n * A⁻¹ := by rw [← zpow_add_one h, sub_add_cancel]
-
 #align matrix.zpow_sub_one Matrix.zpow_sub_one
 
 theorem zpow_add {A : M} (ha : IsUnit A.det) (m n : ℤ) : A ^ (m + n) = A ^ m * A ^ n := by
-  induction' n using Int.induction_on with n ihn n ihn
-  case hz => simp
-  · simp only [← add_assoc, zpow_add_one ha, ihn, mul_assoc]
-  · rw [zpow_sub_one ha, ← mul_assoc, ← ihn, ← zpow_sub_one ha, add_sub_assoc]
+  induction n using Int.induction_on with
+  | hz => simp
+  | hp n ihn => simp only [← add_assoc, zpow_add_one ha, ihn, mul_assoc]
+  | hn n ihn => rw [zpow_sub_one ha, ← mul_assoc, ← ihn, ← zpow_sub_one ha, add_sub_assoc]
 #align matrix.zpow_add Matrix.zpow_add
 
 theorem zpow_add_of_nonpos {A : M} {m n : ℤ} (hm : m ≤ 0) (hn : n ≤ 0) :
@@ -300,7 +296,7 @@ theorem coe_units_zpow (u : Mˣ) : ∀ n : ℤ, ((u ^ n : Mˣ) : M) = (u : M) ^
 theorem zpow_ne_zero_of_isUnit_det [Nonempty n'] [Nontrivial R] {A : M} (ha : IsUnit A.det)
     (z : ℤ) : A ^ z ≠ 0 := by
   have := ha.det_zpow z
-  -- oorting note: was `contrapose! this`
+  -- Porting note: was `contrapose! this`
   revert this
   contrapose!
   rw [ne_eq, not_not]

03fda911

feat: port LinearAlgebra.Matrix.ZPow (#3671)

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

9e33075c

`linear_algebra.matrix.zpow` ⟷ `Mathlib.LinearAlgebra.Matrix.ZPow`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 573

linear_algebra.matrix.zpow ⟷ Mathlib.LinearAlgebra.Matrix.ZPow

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 573

`linear_algebra.matrix.zpow` ⟷ `Mathlib.LinearAlgebra.Matrix.ZPow`