linear_algebra.symplectic_group | 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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ef553359

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -175,10 +175,10 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   use A.det
   refine' (is_unit_det_J l R).hMul_left_cancel _
   rw [mul_one]
-  rw [mem_iff] at hA 
-  apply_fun det at hA 
-  simp only [det_mul, det_transpose] at hA 
-  rw [mul_comm A.det, mul_assoc] at hA 
+  rw [mem_iff] at hA
+  apply_fun det at hA
+  simp only [det_mul, det_transpose] at hA
+  rw [mul_comm A.det, mul_assoc] at hA
   exact hA
 #align symplectic_group.symplectic_det SymplecticGroup.symplectic_det
 -/
@@ -232,7 +232,7 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
   calc
     -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
       simp only [Matrix.mul_assoc, Matrix.neg_mul]
-    _ = (-J l R) ⬝ J l R := by rw [mem_iff'] at hA ; rw [hA]
+    _ = (-J l R) ⬝ J l R := by rw [mem_iff'] at hA; rw [hA]
     _ = (-1 : R) • J l R ⬝ J l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
     _ = (-1 : R) • -1 := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]

ef553359

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) 2022 Matej Penciak. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Matej Penciak, Moritz Doll, Fabien Clery
 -/
-import Mathbin.LinearAlgebra.Matrix.NonsingularInverse
+import LinearAlgebra.Matrix.NonsingularInverse
 
 #align_import linear_algebra.symplectic_group from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"

ef553359

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -100,7 +100,7 @@ variable [Fintype l]
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
     where
   carrier := {A | A ⬝ J l R ⬝ Aᵀ = J l R}
-  mul_mem' := by
+  hMul_mem' := by
     intro a b ha hb
     simp only [mul_eq_mul, Set.mem_setOf_eq, transpose_mul] at *
     rw [← Matrix.mul_assoc, a.mul_assoc, a.mul_assoc, hb]
@@ -173,7 +173,7 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   by
   rw [isUnit_iff_exists_inv]
   use A.det
-  refine' (is_unit_det_J l R).mul_left_cancel _
+  refine' (is_unit_det_J l R).hMul_left_cancel _
   rw [mul_one]
   rw [mem_iff] at hA 
   apply_fun det at hA 
@@ -219,7 +219,7 @@ theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R :=
 instance : Inv (symplecticGroup l R)
     where inv A :=
     ⟨(-J l R) ⬝ (A : Matrix (Sum l l) (Sum l l) R)ᵀ ⬝ J l R,
-      mul_mem (mul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
+      hMul_mem (hMul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
 
 #print SymplecticGroup.coe_inv /-
 theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R :=
@@ -256,10 +256,10 @@ theorem inv_eq_symplectic_inv (A : Matrix (Sum l l) (Sum l l) R) (hA : A ∈ sym
 
 instance : Group (symplecticGroup l R) :=
   { SymplecticGroup.hasInv, Submonoid.toMonoid _ with
-    mul_left_inv := fun A => by
+    hMul_left_inv := fun A => by
       apply Subtype.ext
       simp only [Submonoid.coe_one, Submonoid.coe_mul, Matrix.neg_mul, coe_inv]
-      rw [Matrix.mul_eq_mul, Matrix.neg_mul]
+      rw [Matrix.hMul_eq_hMul, Matrix.neg_mul]
       exact inv_left_mul_aux A.2 }
 
 end SymplecticGroup

ef553359

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) 2022 Matej Penciak. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Matej Penciak, Moritz Doll, Fabien Clery
-
-! This file was ported from Lean 3 source module linear_algebra.symplectic_group
-! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
-! 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.symplectic_group from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
+
 /-!
 # The Symplectic Group

ef553359

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -46,6 +46,7 @@ def J : Matrix (Sum l l) (Sum l l) R :=
 #align matrix.J Matrix.J
 -/
 
+#print Matrix.J_transpose /-
 @[simp]
 theorem J_transpose : (J l R)ᵀ = -J l R :=
   by
@@ -53,23 +54,29 @@ theorem J_transpose : (J l R)ᵀ = -J l R :=
     Matrix.transpose_zero, Matrix.transpose_one, transpose_neg]
   simp [from_blocks]
 #align matrix.J_transpose Matrix.J_transpose
+-/
 
 variable [Fintype l]
 
+#print Matrix.J_squared /-
 theorem J_squared : J l R ⬝ J l R = -1 :=
   by
   rw [J, from_blocks_multiply]
   simp only [Matrix.zero_mul, Matrix.neg_mul, zero_add, neg_zero, Matrix.one_mul, add_zero]
   rw [← neg_zero, ← Matrix.fromBlocks_neg, ← from_blocks_one]
 #align matrix.J_squared Matrix.J_squared
+-/
 
+#print Matrix.J_inv /-
 theorem J_inv : (J l R)⁻¹ = -J l R :=
   by
   refine' Matrix.inv_eq_right_inv _
   rw [Matrix.mul_neg, J_squared]
   exact neg_neg 1
 #align matrix.J_inv Matrix.J_inv
+-/
 
+#print Matrix.J_det_mul_J_det /-
 theorem J_det_mul_J_det : det (J l R) * det (J l R) = 1 :=
   by
   rw [← det_mul, J_squared]
@@ -79,6 +86,7 @@ theorem J_det_mul_J_det : det (J l R) * det (J l R) = 1 :=
   apply Even.neg_one_pow
   exact even_add_self _
 #align matrix.J_det_mul_J_det Matrix.J_det_mul_J_det
+-/
 
 #print Matrix.isUnit_det_J /-
 theorem isUnit_det_J : IsUnit (det (J l R)) :=
@@ -90,6 +98,7 @@ end JMatrixLemmas
 
 variable [Fintype l]
 
+#print Matrix.symplecticGroup /-
 /-- The group of symplectic matrices over a ring `R`. -/
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
     where
@@ -101,6 +110,7 @@ def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
     exact ha
   one_mem' := by simp
 #align matrix.symplectic_group Matrix.symplecticGroup
+-/
 
 end Matrix
 
@@ -110,45 +120,58 @@ variable {l} {R} [DecidableEq l] [Fintype l] [CommRing R]
 
 open Matrix
 
+#print SymplecticGroup.mem_iff /-
 theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
     A ∈ symplecticGroup l R ↔ A ⬝ J l R ⬝ Aᵀ = J l R := by simp [symplectic_group]
 #align symplectic_group.mem_iff SymplecticGroup.mem_iff
+-/
 
+#print SymplecticGroup.coeMatrix /-
 instance coeMatrix : Coe (symplecticGroup l R) (Matrix (Sum l l) (Sum l l) R) := by infer_instance
 #align symplectic_group.coe_matrix SymplecticGroup.coeMatrix
+-/
 
 section SymplecticJ
 
 variable (l) (R)
 
+#print SymplecticGroup.J_mem /-
 theorem J_mem : J l R ∈ symplecticGroup l R :=
   by
   rw [mem_iff, J, from_blocks_multiply, from_blocks_transpose, from_blocks_multiply]
   simp
 #align symplectic_group.J_mem SymplecticGroup.J_mem
+-/
 
+#print SymplecticGroup.symJ /-
 /-- The canonical skew-symmetric matrix as an element in the symplectic group. -/
 def symJ : symplecticGroup l R :=
   ⟨J l R, J_mem l R⟩
 #align symplectic_group.sym_J SymplecticGroup.symJ
+-/
 
 variable {l} {R}
 
+#print SymplecticGroup.coe_J /-
 @[simp]
 theorem coe_J : ↑(symJ l R) = J l R :=
   rfl
 #align symplectic_group.coe_J SymplecticGroup.coe_J
+-/
 
 end SymplecticJ
 
 variable {R} {A : Matrix (Sum l l) (Sum l l) R}
 
+#print SymplecticGroup.neg_mem /-
 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
   by
   rw [mem_iff] at h ⊢
   simp [h]
 #align symplectic_group.neg_mem SymplecticGroup.neg_mem
+-/
 
+#print SymplecticGroup.symplectic_det /-
 theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   by
   rw [isUnit_iff_exists_inv]
@@ -161,7 +184,9 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   rw [mul_comm A.det, mul_assoc] at hA 
   exact hA
 #align symplectic_group.symplectic_det SymplecticGroup.symplectic_det
+-/
 
+#print SymplecticGroup.transpose_mem /-
 theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGroup l R :=
   by
   rw [mem_iff] at hA ⊢
@@ -179,25 +204,33 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
       rw [mul_nonsing_inv_cancel_left _ _ huAT, nonsing_inv_mul_cancel_right _ _ huA]
     _ = J l R := by simp [J_inv]
 #align symplectic_group.transpose_mem SymplecticGroup.transpose_mem
+-/
 
+#print SymplecticGroup.transpose_mem_iff /-
 @[simp]
 theorem transpose_mem_iff : Aᵀ ∈ symplecticGroup l R ↔ A ∈ symplecticGroup l R :=
   ⟨fun hA => by simpa using transpose_mem hA, transpose_mem⟩
 #align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iff
+-/
 
+#print SymplecticGroup.mem_iff' /-
 theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R := by
   rw [← transpose_mem_iff, mem_iff, transpose_transpose]
 #align symplectic_group.mem_iff' SymplecticGroup.mem_iff'
+-/
 
 instance : Inv (symplecticGroup l R)
     where inv A :=
     ⟨(-J l R) ⬝ (A : Matrix (Sum l l) (Sum l l) R)ᵀ ⬝ J l R,
       mul_mem (mul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
 
+#print SymplecticGroup.coe_inv /-
 theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R :=
   rfl
 #align symplectic_group.coe_inv SymplecticGroup.coe_inv
+-/
 
+#print SymplecticGroup.inv_left_mul_aux /-
 theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = 1 :=
   calc
     -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
@@ -207,17 +240,22 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
     _ = (-1 : R) • -1 := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]
 #align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_aux
+-/
 
+#print SymplecticGroup.coe_inv' /-
 theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum l l) R) = A⁻¹ :=
   by
   refine' (coe_inv A).trans (inv_eq_left_inv _).symm
   simp [inv_left_mul_aux, coe_inv]
 #align symplectic_group.coe_inv' SymplecticGroup.coe_inv'
+-/
 
+#print SymplecticGroup.inv_eq_symplectic_inv /-
 theorem inv_eq_symplectic_inv (A : Matrix (Sum l l) (Sum l l) R) (hA : A ∈ symplecticGroup l R) :
     A⁻¹ = (-J l R) ⬝ Aᵀ ⬝ J l R :=
   inv_eq_left_inv (by simp only [Matrix.neg_mul, inv_left_mul_aux hA])
 #align symplectic_group.inv_eq_symplectic_inv SymplecticGroup.inv_eq_symplectic_inv
+-/
 
 instance : Group (symplecticGroup l R) :=
   { SymplecticGroup.hasInv, Submonoid.toMonoid _ with

ef553359

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -178,7 +178,6 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
     _ = -(J l R)⁻¹ := by
       rw [mul_nonsing_inv_cancel_left _ _ huAT, nonsing_inv_mul_cancel_right _ _ huA]
     _ = J l R := by simp [J_inv]
-    
 #align symplectic_group.transpose_mem SymplecticGroup.transpose_mem
 
 @[simp]
@@ -207,7 +206,6 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
     _ = (-1 : R) • J l R ⬝ J l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
     _ = (-1 : R) • -1 := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]
-    
 #align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_aux
 
 theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum l l) R) = A⁻¹ :=

ef553359

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -93,7 +93,7 @@ variable [Fintype l]
 /-- The group of symplectic matrices over a ring `R`. -/
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
     where
-  carrier := { A | A ⬝ J l R ⬝ Aᵀ = J l R }
+  carrier := {A | A ⬝ J l R ⬝ Aᵀ = J l R}
   mul_mem' := by
     intro a b ha hb
     simp only [mul_eq_mul, Set.mem_setOf_eq, transpose_mul] at *
@@ -156,7 +156,7 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   refine' (is_unit_det_J l R).mul_left_cancel _
   rw [mul_one]
   rw [mem_iff] at hA 
-  apply_fun det  at hA 
+  apply_fun det at hA 
   simp only [det_mul, det_transpose] at hA 
   rw [mul_comm A.det, mul_assoc] at hA 
   exact hA

ef553359

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -145,7 +145,7 @@ variable {R} {A : Matrix (Sum l l) (Sum l l) R}
 
 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
   by
-  rw [mem_iff] at h⊢
+  rw [mem_iff] at h ⊢
   simp [h]
 #align symplectic_group.neg_mem SymplecticGroup.neg_mem
 
@@ -155,16 +155,16 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   use A.det
   refine' (is_unit_det_J l R).mul_left_cancel _
   rw [mul_one]
-  rw [mem_iff] at hA
-  apply_fun det  at hA
-  simp only [det_mul, det_transpose] at hA
-  rw [mul_comm A.det, mul_assoc] at hA
+  rw [mem_iff] at hA 
+  apply_fun det  at hA 
+  simp only [det_mul, det_transpose] at hA 
+  rw [mul_comm A.det, mul_assoc] at hA 
   exact hA
 #align symplectic_group.symplectic_det SymplecticGroup.symplectic_det
 
 theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGroup l R :=
   by
-  rw [mem_iff] at hA⊢
+  rw [mem_iff] at hA ⊢
   rw [transpose_transpose]
   have huA := symplectic_det hA
   have huAT : IsUnit Aᵀ.det := by
@@ -203,7 +203,7 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
   calc
     -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
       simp only [Matrix.mul_assoc, Matrix.neg_mul]
-    _ = (-J l R) ⬝ J l R := by rw [mem_iff'] at hA; rw [hA]
+    _ = (-J l R) ⬝ J l R := by rw [mem_iff'] at hA ; rw [hA]
     _ = (-1 : R) • J l R ⬝ J l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
     _ = (-1 : R) • -1 := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]

ef553359

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -29,7 +29,7 @@ This file defines the symplectic group and proves elementary properties.
 -/
 
 
-open Matrix
+open scoped Matrix
 
 variable {l R : Type _}

ef553359

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -46,12 +46,6 @@ def J : Matrix (Sum l l) (Sum l l) R :=
 #align matrix.J Matrix.J
 -/
 
-/- warning: matrix.J_transpose -> Matrix.J_transpose is a dubious translation:
-lean 3 declaration is
-  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasNeg.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_2))))))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2))
-but is expected to have type
-  forall (l : Type.{u2}) (R : Type.{u1}) [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : CommRing.{u1} R], Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2))
-Case conversion may be inaccurate. Consider using '#align matrix.J_transpose Matrix.J_transposeₓ'. -/
 @[simp]
 theorem J_transpose : (J l R)ᵀ = -J l R :=
   by
@@ -62,12 +56,6 @@ theorem J_transpose : (J l R)ᵀ = -J l R :=
 
 variable [Fintype l]
 
-/- warning: matrix.J_squared -> Matrix.J_squared is a dubious translation:
-lean 3 declaration is
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 theorem J_squared : J l R ⬝ J l R = -1 :=
   by
   rw [J, from_blocks_multiply]
@@ -75,12 +63,6 @@ theorem J_squared : J l R ⬝ J l R = -1 :=
   rw [← neg_zero, ← Matrix.fromBlocks_neg, ← from_blocks_one]
 #align matrix.J_squared Matrix.J_squared
 
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 theorem J_inv : (J l R)⁻¹ = -J l R :=
   by
   refine' Matrix.inv_eq_right_inv _
@@ -88,12 +70,6 @@ theorem J_inv : (J l R)⁻¹ = -J l R :=
   exact neg_neg 1
 #align matrix.J_inv Matrix.J_inv
 
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 theorem J_det_mul_J_det : det (J l R) * det (J l R) = 1 :=
   by
   rw [← det_mul, J_squared]
@@ -114,12 +90,6 @@ end JMatrixLemmas
 
 variable [Fintype l]
 
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 /-- The group of symplectic matrices over a ring `R`. -/
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
     where
@@ -140,19 +110,10 @@ variable {l} {R} [DecidableEq l] [Fintype l] [CommRing R]
 
 open Matrix
 
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.mem_iff SymplecticGroup.mem_iffₓ'. -/
 theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
     A ∈ symplecticGroup l R ↔ A ⬝ J l R ⬝ Aᵀ = J l R := by simp [symplectic_group]
 #align symplectic_group.mem_iff SymplecticGroup.mem_iff
 
-/- warning: symplectic_group.coe_matrix -> SymplecticGroup.coeMatrix is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_matrix SymplecticGroup.coeMatrixₓ'. -/
 instance coeMatrix : Coe (symplecticGroup l R) (Matrix (Sum l l) (Sum l l) R) := by infer_instance
 #align symplectic_group.coe_matrix SymplecticGroup.coeMatrix
 
@@ -160,24 +121,12 @@ section SymplecticJ
 
 variable (l) (R)
 
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.J_mem SymplecticGroup.J_memₓ'. -/
 theorem J_mem : J l R ∈ symplecticGroup l R :=
   by
   rw [mem_iff, J, from_blocks_multiply, from_blocks_transpose, from_blocks_multiply]
   simp
 #align symplectic_group.J_mem SymplecticGroup.J_mem
 
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 /-- The canonical skew-symmetric matrix as an element in the symplectic group. -/
 def symJ : symplecticGroup l R :=
   ⟨J l R, J_mem l R⟩
@@ -185,9 +134,6 @@ def symJ : symplecticGroup l R :=
 
 variable {l} {R}
 
-/- warning: symplectic_group.coe_J -> SymplecticGroup.coe_J is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_J SymplecticGroup.coe_Jₓ'. -/
 @[simp]
 theorem coe_J : ↑(symJ l R) = J l R :=
   rfl
@@ -197,21 +143,12 @@ end SymplecticJ
 
 variable {R} {A : Matrix (Sum l l) (Sum l l) R}
 
-/- warning: symplectic_group.neg_mem -> SymplecticGroup.neg_mem is a dubious translation:
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 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
   by
   rw [mem_iff] at h⊢
   simp [h]
 #align symplectic_group.neg_mem SymplecticGroup.neg_mem
 
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.symplectic_det SymplecticGroup.symplectic_detₓ'. -/
 theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   by
   rw [isUnit_iff_exists_inv]
@@ -225,12 +162,6 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   exact hA
 #align symplectic_group.symplectic_det SymplecticGroup.symplectic_det
 
-/- warning: symplectic_group.transpose_mem -> SymplecticGroup.transpose_mem is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.transpose_mem SymplecticGroup.transpose_memₓ'. -/
 theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGroup l R :=
   by
   rw [mem_iff] at hA⊢
@@ -250,23 +181,11 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
     
 #align symplectic_group.transpose_mem SymplecticGroup.transpose_mem
 
-/- warning: symplectic_group.transpose_mem_iff -> SymplecticGroup.transpose_mem_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iffₓ'. -/
 @[simp]
 theorem transpose_mem_iff : Aᵀ ∈ symplecticGroup l R ↔ A ∈ symplecticGroup l R :=
   ⟨fun hA => by simpa using transpose_mem hA, transpose_mem⟩
 #align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iff
 
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.mem_iff' SymplecticGroup.mem_iff'ₓ'. -/
 theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R := by
   rw [← transpose_mem_iff, mem_iff, transpose_transpose]
 #align symplectic_group.mem_iff' SymplecticGroup.mem_iff'
@@ -276,16 +195,10 @@ instance : Inv (symplecticGroup l R)
     ⟨(-J l R) ⬝ (A : Matrix (Sum l l) (Sum l l) R)ᵀ ⬝ J l R,
       mul_mem (mul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
 
-/- warning: symplectic_group.coe_inv -> SymplecticGroup.coe_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_inv SymplecticGroup.coe_invₓ'. -/
 theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R :=
   rfl
 #align symplectic_group.coe_inv SymplecticGroup.coe_inv
 
-/- warning: symplectic_group.inv_left_mul_aux -> SymplecticGroup.inv_left_mul_aux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_auxₓ'. -/
 theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = 1 :=
   calc
     -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
@@ -297,21 +210,12 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
     
 #align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_aux
 
-/- warning: symplectic_group.coe_inv' -> SymplecticGroup.coe_inv' is a dubious translation:
-<too large>
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 theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum l l) R) = A⁻¹ :=
   by
   refine' (coe_inv A).trans (inv_eq_left_inv _).symm
   simp [inv_left_mul_aux, coe_inv]
 #align symplectic_group.coe_inv' SymplecticGroup.coe_inv'
 
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-Case conversion may be inaccurate. Consider using '#align symplectic_group.inv_eq_symplectic_inv SymplecticGroup.inv_eq_symplectic_invₓ'. -/
 theorem inv_eq_symplectic_inv (A : Matrix (Sum l l) (Sum l l) R) (hA : A ∈ symplecticGroup l R) :
     A⁻¹ = (-J l R) ⬝ Aᵀ ⬝ J l R :=
   inv_eq_left_inv (by simp only [Matrix.neg_mul, inv_left_mul_aux hA])

ef553359

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -240,9 +240,7 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
     rw [Matrix.det_transpose]
     exact huA
   calc
-    Aᵀ ⬝ J l R ⬝ A = (-Aᵀ) ⬝ (J l R)⁻¹ ⬝ A := by
-      rw [J_inv]
-      simp
+    Aᵀ ⬝ J l R ⬝ A = (-Aᵀ) ⬝ (J l R)⁻¹ ⬝ A := by rw [J_inv]; simp
     _ = (-Aᵀ) ⬝ (A ⬝ J l R ⬝ Aᵀ)⁻¹ ⬝ A := by rw [hA]
     _ = (-Aᵀ ⬝ (Aᵀ⁻¹ ⬝ (J l R)⁻¹)) ⬝ A⁻¹ ⬝ A := by
       simp only [Matrix.mul_inv_rev, Matrix.mul_assoc, Matrix.neg_mul]
@@ -292,9 +290,7 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
   calc
     -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
       simp only [Matrix.mul_assoc, Matrix.neg_mul]
-    _ = (-J l R) ⬝ J l R := by
-      rw [mem_iff'] at hA
-      rw [hA]
+    _ = (-J l R) ⬝ J l R := by rw [mem_iff'] at hA; rw [hA]
     _ = (-1 : R) • J l R ⬝ J l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
     _ = (-1 : R) • -1 := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]

ef553359

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -151,10 +151,7 @@ theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
 #align symplectic_group.mem_iff SymplecticGroup.mem_iff
 
 /- warning: symplectic_group.coe_matrix -> SymplecticGroup.coeMatrix is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_matrix SymplecticGroup.coeMatrixₓ'. -/
 instance coeMatrix : Coe (symplecticGroup l R) (Matrix (Sum l l) (Sum l l) R) := by infer_instance
 #align symplectic_group.coe_matrix SymplecticGroup.coeMatrix
@@ -189,10 +186,7 @@ def symJ : symplecticGroup l R :=
 variable {l} {R}
 
 /- warning: symplectic_group.coe_J -> SymplecticGroup.coe_J is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_J SymplecticGroup.coe_Jₓ'. -/
 @[simp]
 theorem coe_J : ↑(symJ l R) = J l R :=
@@ -204,10 +198,7 @@ end SymplecticJ
 variable {R} {A : Matrix (Sum l l) (Sum l l) R}
 
 /- warning: symplectic_group.neg_mem -> SymplecticGroup.neg_mem is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align symplectic_group.neg_mem SymplecticGroup.neg_memₓ'. -/
 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
   by
@@ -288,20 +279,14 @@ instance : Inv (symplecticGroup l R)
       mul_mem (mul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
 
 /- warning: symplectic_group.coe_inv -> SymplecticGroup.coe_inv is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_inv SymplecticGroup.coe_invₓ'. -/
 theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R :=
   rfl
 #align symplectic_group.coe_inv SymplecticGroup.coe_inv
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_auxₓ'. -/
 theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = 1 :=
   calc
@@ -317,10 +302,7 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
 #align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_aux
 
 /- warning: symplectic_group.coe_inv' -> SymplecticGroup.coe_inv' is a dubious translation:
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (SymplecticGroup.hasInv.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3) A)) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.inv.{u2, u1} (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) A))
+<too large>
 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_inv' SymplecticGroup.coe_inv'ₓ'. -/
 theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum l l) R) = A⁻¹ :=
   by

ef553359

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -66,7 +66,7 @@ variable [Fintype l]
 lean 3 declaration is
   forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_3 _inst_3) (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} R (NonUnitalNonAssocRing.toAddCommGroup.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasNeg.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_2))))))) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasOne.{u2, u1} (Sum.{u1, u1} l l) R (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) 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_2)))))) (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_2))))))))))
 but is expected to have type
-  forall (l : Type.{u2}) (R : Type.{u1}) [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : CommRing.{u1} R] [_inst_3 : Fintype.{u2} l], Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_3 _inst_3) (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_2))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.one.{u1, u2} (Sum.{u2, u2} l l) R (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))))))
+  forall (l : Type.{u2}) (R : Type.{u1}) [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : CommRing.{u1} R] [_inst_3 : Fintype.{u2} l], Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_3 _inst_3) (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_2))))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_2))) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.one.{u1, u2} (Sum.{u2, u2} l l) R (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)))))))
 Case conversion may be inaccurate. Consider using '#align matrix.J_squared Matrix.J_squaredₓ'. -/
 theorem J_squared : J l R ⬝ J l R = -1 :=
   by
@@ -92,7 +92,7 @@ theorem J_inv : (J l R)⁻¹ = -J l R :=
 lean 3 declaration is
   forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Eq.{succ u2} R (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (Distrib.toHasMul.{u2} R (Ring.toDistrib.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b) (Sum.fintype.{u1, u1} l l _inst_3 _inst_3) R _inst_2 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b) (Sum.fintype.{u1, u1} l l _inst_3 _inst_3) R _inst_2 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2))) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_2))))))))
 but is expected to have type
-  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Eq.{succ u2} R (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))))) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u1, u1} l l _inst_3 _inst_3) R _inst_2 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u1, u1} l l _inst_3 _inst_3) R _inst_2 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2))) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))
+  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Eq.{succ u2} R (HMul.hMul.{u2, u2, u2} R R R (instHMul.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))))) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u1, u1} l l _inst_3 _inst_3) R _inst_2 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2)) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u1, u1} l l _inst_3 _inst_3) R _inst_2 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2))) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align matrix.J_det_mul_J_det Matrix.J_det_mul_J_detₓ'. -/
 theorem J_det_mul_J_det : det (J l R) * det (J l R) = 1 :=
   by
@@ -118,7 +118,7 @@ variable [Fintype l]
 lean 3 declaration is
   forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (Sum.fintype.{u1, u1} l l _inst_3 _inst_3) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))
 but is expected to have type
-  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (instFintypeSum.{u1, u1} l l _inst_3 _inst_3) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))
+  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (instFintypeSum.{u1, u1} l l _inst_3 _inst_3) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))
 Case conversion may be inaccurate. Consider using '#align matrix.symplectic_group Matrix.symplecticGroupₓ'. -/
 /-- The group of symplectic matrices over a ring `R`. -/
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
@@ -144,7 +144,7 @@ open Matrix
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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 (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A)) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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 (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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 (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.mem_iff SymplecticGroup.mem_iffₓ'. -/
 theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
     A ∈ symplecticGroup l R ↔ A ⬝ J l R ⬝ Aᵀ = J l R := by simp [symplectic_group]
@@ -154,7 +154,7 @@ theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Coe.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R)
 but is expected to have type
-  forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Coe.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (fun (x : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R)
+  forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Coe.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (fun (x : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R)
 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_matrix SymplecticGroup.coeMatrixₓ'. -/
 instance coeMatrix : Coe (symplecticGroup l R) (Matrix (Sum l l) (Sum l l) R) := by infer_instance
 #align symplectic_group.coe_matrix SymplecticGroup.coeMatrix
@@ -167,7 +167,7 @@ variable (l) (R)
 lean 3 declaration is
   forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)
 but is expected to have type
-  forall (l : Type.{u2}) (R : Type.{u1}) [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R], Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)
+  forall (l : Type.{u2}) (R : Type.{u1}) [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R], Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)
 Case conversion may be inaccurate. Consider using '#align symplectic_group.J_mem SymplecticGroup.J_memₓ'. -/
 theorem J_mem : J l R ∈ symplecticGroup l R :=
   by
@@ -179,7 +179,7 @@ theorem J_mem : J l R ∈ symplecticGroup l R :=
 lean 3 declaration is
   forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)
 but is expected to have type
-  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (fun (x : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Subtype.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (fun (x : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) => Membership.mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submonoid.{max u2 u1} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.instSetLikeSubmonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_3))) (instFintypeSum.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.instDecidableEqSum.{u1, u1} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.sym_J SymplecticGroup.symJₓ'. -/
 /-- The canonical skew-symmetric matrix as an element in the symplectic group. -/
 def symJ : symplecticGroup l R :=
@@ -192,7 +192,7 @@ variable {l} {R}
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R], Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) 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) (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (coeBase.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (SymplecticGroup.coeMatrix.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)))) (SymplecticGroup.symJ.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R], Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (SymplecticGroup.symJ.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R], Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (SymplecticGroup.symJ.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)
 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_J SymplecticGroup.coe_Jₓ'. -/
 @[simp]
 theorem coe_J : ↑(symJ l R) = J l R :=
@@ -207,7 +207,7 @@ variable {R} {A : Matrix (Sum l l) (Sum l l) R}
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasNeg.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) A) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.neg_mem SymplecticGroup.neg_memₓ'. -/
 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
   by
@@ -219,7 +219,7 @@ theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (IsUnit.{u2} R (Ring.toMonoid.{u2} R (CommRing.toRing.{u2} R _inst_3)) (Matrix.det.{u2, u1} (Sum.{u1, u1} l l) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) R _inst_3 A))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (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} (Sum.{u2, u2} l l) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) R _inst_3 A))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (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} (Sum.{u2, u2} l l) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) R _inst_3 A))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.symplectic_det SymplecticGroup.symplectic_detₓ'. -/
 theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   by
@@ -238,7 +238,7 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.transpose_mem SymplecticGroup.transpose_memₓ'. -/
 theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGroup l R :=
   by
@@ -265,7 +265,7 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iffₓ'. -/
 @[simp]
 theorem transpose_mem_iff : Aᵀ ∈ symplecticGroup l R ↔ A ∈ symplecticGroup l R :=
@@ -276,7 +276,7 @@ theorem transpose_mem_iff : Aᵀ ∈ symplecticGroup l R ↔ A ∈ symplecticGro
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, Iff (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) A) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) A) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, Iff (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) A) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.mem_iff' SymplecticGroup.mem_iff'ₓ'. -/
 theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R := by
   rw [← transpose_mem_iff, mem_iff, transpose_transpose]
@@ -291,7 +291,7 @@ instance : Inv (symplecticGroup l R)
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] (A : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} 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(NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (SymplecticGroup.coeMatrix.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)))) A))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (Inv.inv.{max u2 u1} (Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (SymplecticGroup.hasInv.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3) A)) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) A))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) 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(Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l 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u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => 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(Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) A))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_inv SymplecticGroup.coe_invₓ'. -/
 theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R :=
   rfl
@@ -301,7 +301,7 @@ theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max 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u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasNeg.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A)) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) A)) (OfNat.ofNat.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) 1 (OfNat.mk.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) 1 (One.one.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasOne.{u2, u1} (Sum.{u1, u1} l l) R (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) 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 {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) A)) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.one.{u1, u2} (Sum.{u2, u2} l l) R (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) 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 {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) A)) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.one.{u1, u2} (Sum.{u2, u2} l l) R (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) 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 symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_auxₓ'. -/
 theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = 1 :=
   calc
@@ -320,7 +320,7 @@ theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] (A : coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) Type.{max u1 u2} (SetLike.hasCoeToSort.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} 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R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (HasLiftT.mk.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : 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(Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (CoeTCₓ.coe.{succ (max u1 u2), succ (max u1 u2)} 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(NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (coeBase.{succ (max u1 u2), succ (max u1 u2)} (coeSort.{succ (max u1 u2), succ (succ (max u1 u2))} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R 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(NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (SymplecticGroup.coeMatrix.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)))) A))
 but is expected to have type
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(MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (Inv.inv.{max u2 u1} (Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (SymplecticGroup.hasInv.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3) A)) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.inv.{u2, u1} (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) A))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))), Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (Inv.inv.{max u2 u1} (Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) x (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) (SymplecticGroup.hasInv.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3) A)) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.inv.{u2, u1} (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) (Subtype.val.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Set.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) (Set.instMembershipSet.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R)) x (SetLike.coe.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))) A))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_inv' SymplecticGroup.coe_inv'ₓ'. -/
 theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum l l) R) = A⁻¹ :=
   by
@@ -332,7 +332,7 @@ theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum
 lean 3 declaration is
   forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R), (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasInv.{u1, u2} (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) A) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasNeg.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A)) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)))
 but is expected to have type
-  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R), (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.inv.{u2, u1} (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) A) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)))
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R), (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.inv.{u2, u1} (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) A) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align symplectic_group.inv_eq_symplectic_inv SymplecticGroup.inv_eq_symplectic_invₓ'. -/
 theorem inv_eq_symplectic_inv (A : Matrix (Sum l l) (Sum l l) R) (hA : A ∈ symplecticGroup l R) :
     A⁻¹ = (-J l R) ⬝ Aᵀ ⬝ J l R :=

ef553359

bump to nightly-2023-05-03-02

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

5ced3cdd

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Matej Penciak, Moritz Doll, Fabien Clery
 
 ! This file was ported from Lean 3 source module linear_algebra.symplectic_group
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
 ! 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
 /-!
 # The Symplectic Group
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the symplectic group and proves elementary properties.
 
 ## Main Definitions

70fd9563

bump to nightly-2023-04-29-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/a4f99eae998680d3a2c240da4a2b16354c85ee49

739f838b

Diff

@@ -36,36 +36,62 @@ variable (l) [DecidableEq l] (R) [CommRing R]
 
 section JMatrixLemmas
 
+#print Matrix.J /-
 /-- The matrix defining the canonical skew-symmetric bilinear form. -/
-def j : Matrix (Sum l l) (Sum l l) R :=
+def J : Matrix (Sum l l) (Sum l l) R :=
   Matrix.fromBlocks 0 (-1) 1 0
-#align matrix.J Matrix.j
+#align matrix.J Matrix.J
+-/
 
+/- warning: matrix.J_transpose -> Matrix.J_transpose is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align matrix.J_transpose Matrix.J_transposeₓ'. -/
 @[simp]
-theorem j_transpose : (j l R)ᵀ = -j l R :=
+theorem J_transpose : (J l R)ᵀ = -J l R :=
   by
   rw [J, from_blocks_transpose, ← neg_one_smul R (from_blocks _ _ _ _), from_blocks_smul,
     Matrix.transpose_zero, Matrix.transpose_one, transpose_neg]
   simp [from_blocks]
-#align matrix.J_transpose Matrix.j_transpose
+#align matrix.J_transpose Matrix.J_transpose
 
 variable [Fintype l]
 
-theorem j_squared : j l R ⬝ j l R = -1 :=
+/- warning: matrix.J_squared -> Matrix.J_squared is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.J_squared Matrix.J_squaredₓ'. -/
+theorem J_squared : J l R ⬝ J l R = -1 :=
   by
   rw [J, from_blocks_multiply]
   simp only [Matrix.zero_mul, Matrix.neg_mul, zero_add, neg_zero, Matrix.one_mul, add_zero]
   rw [← neg_zero, ← Matrix.fromBlocks_neg, ← from_blocks_one]
-#align matrix.J_squared Matrix.j_squared
-
-theorem j_inv : (j l R)⁻¹ = -j l R :=
+#align matrix.J_squared Matrix.J_squared
+
+/- warning: matrix.J_inv -> Matrix.J_inv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.J_inv Matrix.J_invₓ'. -/
+theorem J_inv : (J l R)⁻¹ = -J l R :=
   by
   refine' Matrix.inv_eq_right_inv _
   rw [Matrix.mul_neg, J_squared]
   exact neg_neg 1
-#align matrix.J_inv Matrix.j_inv
-
-theorem j_det_mul_j_det : det (j l R) * det (j l R) = 1 :=
+#align matrix.J_inv Matrix.J_inv
+
+/- warning: matrix.J_det_mul_J_det -> Matrix.J_det_mul_J_det is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align matrix.J_det_mul_J_det Matrix.J_det_mul_J_detₓ'. -/
+theorem J_det_mul_J_det : det (J l R) * det (J l R) = 1 :=
   by
   rw [← det_mul, J_squared]
   rw [← one_smul R (-1 : Matrix _ _ R)]
@@ -73,20 +99,28 @@ theorem j_det_mul_j_det : det (j l R) * det (j l R) = 1 :=
   simp only [Fintype.card_sum, det_one, mul_one]
   apply Even.neg_one_pow
   exact even_add_self _
-#align matrix.J_det_mul_J_det Matrix.j_det_mul_j_det
+#align matrix.J_det_mul_J_det Matrix.J_det_mul_J_det
 
-theorem isUnit_det_j : IsUnit (det (j l R)) :=
-  isUnit_iff_exists_inv.mpr ⟨det (j l R), j_det_mul_j_det _ _⟩
-#align matrix.is_unit_det_J Matrix.isUnit_det_j
+#print Matrix.isUnit_det_J /-
+theorem isUnit_det_J : IsUnit (det (J l R)) :=
+  isUnit_iff_exists_inv.mpr ⟨det (J l R), J_det_mul_J_det _ _⟩
+#align matrix.is_unit_det_J Matrix.isUnit_det_J
+-/
 
 end JMatrixLemmas
 
 variable [Fintype l]
 
+/- warning: matrix.symplectic_group -> Matrix.symplecticGroup is a dubious translation:
+lean 3 declaration is
+  forall (l : Type.{u1}) (R : Type.{u2}) [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : CommRing.{u2} R] [_inst_3 : Fintype.{u1} l], Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (Sum.fintype.{u1, u1} l l _inst_3 _inst_3) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align matrix.symplectic_group Matrix.symplecticGroupₓ'. -/
 /-- The group of symplectic matrices over a ring `R`. -/
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R)
     where
-  carrier := { A | A ⬝ j l R ⬝ Aᵀ = j l R }
+  carrier := { A | A ⬝ J l R ⬝ Aᵀ = J l R }
   mul_mem' := by
     intro a b ha hb
     simp only [mul_eq_mul, Set.mem_setOf_eq, transpose_mul] at *
@@ -103,10 +137,22 @@ variable {l} {R} [DecidableEq l] [Fintype l] [CommRing R]
 
 open Matrix
 
+/- warning: symplectic_group.mem_iff -> SymplecticGroup.mem_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.mem_iff SymplecticGroup.mem_iffₓ'. -/
 theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
-    A ∈ symplecticGroup l R ↔ A ⬝ j l R ⬝ Aᵀ = j l R := by simp [symplectic_group]
+    A ∈ symplecticGroup l R ↔ A ⬝ J l R ⬝ Aᵀ = J l R := by simp [symplectic_group]
 #align symplectic_group.mem_iff SymplecticGroup.mem_iff
 
+/- warning: symplectic_group.coe_matrix -> SymplecticGroup.coeMatrix is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_matrix SymplecticGroup.coeMatrixₓ'. -/
 instance coeMatrix : Coe (symplecticGroup l R) (Matrix (Sum l l) (Sum l l) R) := by infer_instance
 #align symplectic_group.coe_matrix SymplecticGroup.coeMatrix
 
@@ -114,34 +160,64 @@ section SymplecticJ
 
 variable (l) (R)
 
-theorem j_mem : j l R ∈ symplecticGroup l R :=
+/- warning: symplectic_group.J_mem -> SymplecticGroup.J_mem is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.J_mem SymplecticGroup.J_memₓ'. -/
+theorem J_mem : J l R ∈ symplecticGroup l R :=
   by
   rw [mem_iff, J, from_blocks_multiply, from_blocks_transpose, from_blocks_multiply]
   simp
-#align symplectic_group.J_mem SymplecticGroup.j_mem
-
+#align symplectic_group.J_mem SymplecticGroup.J_mem
+
+/- warning: symplectic_group.sym_J -> SymplecticGroup.symJ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.sym_J SymplecticGroup.symJₓ'. -/
 /-- The canonical skew-symmetric matrix as an element in the symplectic group. -/
 def symJ : symplecticGroup l R :=
-  ⟨j l R, j_mem l R⟩
+  ⟨J l R, J_mem l R⟩
 #align symplectic_group.sym_J SymplecticGroup.symJ
 
 variable {l} {R}
 
+/- warning: symplectic_group.coe_J -> SymplecticGroup.coe_J 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 symplectic_group.coe_J SymplecticGroup.coe_Jₓ'. -/
 @[simp]
-theorem coe_j : ↑(symJ l R) = j l R :=
+theorem coe_J : ↑(symJ l R) = J l R :=
   rfl
-#align symplectic_group.coe_J SymplecticGroup.coe_j
+#align symplectic_group.coe_J SymplecticGroup.coe_J
 
 end SymplecticJ
 
 variable {R} {A : Matrix (Sum l l) (Sum l l) R}
 
+/- warning: symplectic_group.neg_mem -> SymplecticGroup.neg_mem is a dubious translation:
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u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+Case conversion may be inaccurate. Consider using '#align symplectic_group.neg_mem SymplecticGroup.neg_memₓ'. -/
 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R :=
   by
   rw [mem_iff] at h⊢
   simp [h]
 #align symplectic_group.neg_mem SymplecticGroup.neg_mem
 
+/- warning: symplectic_group.symplectic_det -> SymplecticGroup.symplectic_det is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (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} (Sum.{u2, u2} l l) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) R _inst_3 A))
+Case conversion may be inaccurate. Consider using '#align symplectic_group.symplectic_det SymplecticGroup.symplectic_detₓ'. -/
 theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   by
   rw [isUnit_iff_exists_inv]
@@ -155,6 +231,12 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A :=
   exact hA
 #align symplectic_group.symplectic_det SymplecticGroup.symplectic_det
 
+/- warning: symplectic_group.transpose_mem -> SymplecticGroup.transpose_mem is a dubious translation:
+lean 3 declaration is
+  forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] {A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R}, (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+but is expected to have type
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] {A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R}, (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A) (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2))
+Case conversion may be inaccurate. Consider using '#align symplectic_group.transpose_mem SymplecticGroup.transpose_memₓ'. -/
 theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGroup l R :=
   by
   rw [mem_iff] at hA⊢
@@ -176,45 +258,81 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
     
 #align symplectic_group.transpose_mem SymplecticGroup.transpose_mem
 
+/- warning: symplectic_group.transpose_mem_iff -> SymplecticGroup.transpose_mem_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iffₓ'. -/
 @[simp]
 theorem transpose_mem_iff : Aᵀ ∈ symplecticGroup l R ↔ A ∈ symplecticGroup l R :=
   ⟨fun hA => by simpa using transpose_mem hA, transpose_mem⟩
 #align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iff
 
-theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ j l R ⬝ A = j l R := by
+/- warning: symplectic_group.mem_iff' -> SymplecticGroup.mem_iff' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.mem_iff' SymplecticGroup.mem_iff'ₓ'. -/
+theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R := by
   rw [← transpose_mem_iff, mem_iff, transpose_transpose]
 #align symplectic_group.mem_iff' SymplecticGroup.mem_iff'
 
 instance : Inv (symplecticGroup l R)
     where inv A :=
-    ⟨(-j l R) ⬝ (A : Matrix (Sum l l) (Sum l l) R)ᵀ ⬝ j l R,
-      mul_mem (mul_mem (neg_mem <| j_mem _ _) <| transpose_mem A.2) <| j_mem _ _⟩
-
-theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-j l R) ⬝ (↑A)ᵀ ⬝ j l R :=
+    ⟨(-J l R) ⬝ (A : Matrix (Sum l l) (Sum l l) R)ᵀ ⬝ J l R,
+      mul_mem (mul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
+
+/- warning: symplectic_group.coe_inv -> SymplecticGroup.coe_inv 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 symplectic_group.coe_inv SymplecticGroup.coe_invₓ'. -/
+theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R :=
   rfl
 #align symplectic_group.coe_inv SymplecticGroup.coe_inv
 
-theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -j l R ⬝ Aᵀ ⬝ j l R ⬝ A = 1 :=
+/- warning: symplectic_group.inv_left_mul_aux -> SymplecticGroup.inv_left_mul_aux is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_auxₓ'. -/
+theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = 1 :=
   calc
-    -j l R ⬝ Aᵀ ⬝ j l R ⬝ A = (-j l R) ⬝ (Aᵀ ⬝ j l R ⬝ A) := by
+    -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
       simp only [Matrix.mul_assoc, Matrix.neg_mul]
-    _ = (-j l R) ⬝ j l R := by
+    _ = (-J l R) ⬝ J l R := by
       rw [mem_iff'] at hA
       rw [hA]
-    _ = (-1 : R) • j l R ⬝ j l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
+    _ = (-1 : R) • J l R ⬝ J l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
     _ = (-1 : R) • -1 := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]
     
 #align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_aux
 
+/- warning: symplectic_group.coe_inv' -> SymplecticGroup.coe_inv' is a dubious translation:
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u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) l (fun (a : l) (b : l) => (fun (a : l) (b : l) => _inst_1 a b) a b) a b)))))) (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (SymplecticGroup.coeMatrix.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_2 _inst_3)))) A))
+but is expected to have type
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Subtype.{succ (max u2 u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (fun (x : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) => Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun 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+Case conversion may be inaccurate. Consider using '#align symplectic_group.coe_inv' SymplecticGroup.coe_inv'ₓ'. -/
 theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum l l) R) = A⁻¹ :=
   by
   refine' (coe_inv A).trans (inv_eq_left_inv _).symm
   simp [inv_left_mul_aux, coe_inv]
 #align symplectic_group.coe_inv' SymplecticGroup.coe_inv'
 
+/- warning: symplectic_group.inv_eq_symplectic_inv -> SymplecticGroup.inv_eq_symplectic_inv is a dubious translation:
+lean 3 declaration is
+  forall {l : Type.{u1}} {R : Type.{u2}} [_inst_1 : DecidableEq.{succ u1} l] [_inst_2 : Fintype.{u1} l] [_inst_3 : CommRing.{u2} R] (A : Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R), (Membership.Mem.{max u1 u2, max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submonoid.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Submonoid.setLike.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (MulZeroOneClass.toMulOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.nonAssocSemiring.{u2, u1} (Sum.{u1, u1} l l) R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_3))) (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{succ (max u1 u2)} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Inv.inv.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasInv.{u1, u2} (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _inst_2) (fun (a : Sum.{u1, u1} l l) (b : Sum.{u1, u1} l l) => Sum.decidableEq.{u1, u1} l (fun (a : l) (b : l) => _inst_1 a b) l (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) A) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Matrix.mul.{u2, u1, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (Sum.fintype.{u1, u1} l l _inst_2 _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))))) (Neg.neg.{max u1 u2} (Matrix.{u1, u1, u2} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R) (Matrix.hasNeg.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R (SubNegMonoid.toHasNeg.{u2} R (AddGroup.toSubNegMonoid.{u2} R (AddGroupWithOne.toAddGroup.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_3))))))) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u2, u1, u1} (Sum.{u1, u1} l l) (Sum.{u1, u1} l l) R A)) (Matrix.J.{u1, u2} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)))
+but is expected to have type
+  forall {l : Type.{u2}} {R : Type.{u1}} [_inst_1 : DecidableEq.{succ u2} l] [_inst_2 : Fintype.{u2} l] [_inst_3 : CommRing.{u1} R] (A : Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R), (Membership.mem.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (SetLike.instMembership.{max u2 u1, max u2 u1} (Submonoid.{max u1 u2} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b))))) (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Submonoid.instSetLikeSubmonoid.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (MulZeroOneClass.toMulOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (NonAssocSemiring.toMulZeroOneClass.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.nonAssocSemiring.{u1, u2} (Sum.{u2, u2} l l) R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_3))) (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b)))))) A (Matrix.symplecticGroup.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3 _inst_2)) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Inv.inv.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.inv.{u2, u1} (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _inst_2) (fun (a : Sum.{u2, u2} l l) (b : Sum.{u2, u2} l l) => Sum.instDecidableEqSum.{u2, u2} l l (fun (a : l) (b : l) => _inst_1 a b) (fun (a : l) (b : l) => _inst_1 a b) a b) _inst_3) A) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Matrix.mul.{u1, u2, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (instFintypeSum.{u2, u2} l l _inst_2 _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))))) (Neg.neg.{max u2 u1} (Matrix.{u2, u2, u1} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R) (Matrix.neg.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R (Ring.toNeg.{u1} R (CommRing.toRing.{u1} R _inst_3))) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)) (Matrix.transpose.{u1, u2, u2} (Sum.{u2, u2} l l) (Sum.{u2, u2} l l) R A)) (Matrix.J.{u2, u1} l R (fun (a : l) (b : l) => _inst_1 a b) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align symplectic_group.inv_eq_symplectic_inv SymplecticGroup.inv_eq_symplectic_invₓ'. -/
 theorem inv_eq_symplectic_inv (A : Matrix (Sum l l) (Sum l l) R) (hA : A ∈ symplecticGroup l R) :
-    A⁻¹ = (-j l R) ⬝ Aᵀ ⬝ j l R :=
+    A⁻¹ = (-J l R) ⬝ Aᵀ ⬝ J l R :=
   inv_eq_left_inv (by simp only [Matrix.neg_mul, inv_left_mul_aux hA])
 #align symplectic_group.inv_eq_symplectic_inv SymplecticGroup.inv_eq_symplectic_inv

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

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

@@ -49,7 +49,7 @@ set_option linter.uppercaseLean3 false in
 
 variable [Fintype l]
 
-theorem J_squared : J l R ⬝ J l R = -1 := by
+theorem J_squared : J l R * J l R = -1 := by
   rw [J, fromBlocks_multiply]
   simp only [Matrix.zero_mul, Matrix.neg_mul, zero_add, neg_zero, Matrix.one_mul, add_zero]
   rw [← neg_zero, ← Matrix.fromBlocks_neg, ← fromBlocks_one]
@@ -82,9 +82,9 @@ variable [Fintype l]
 
 /-- The group of symplectic matrices over a ring `R`. -/
 def symplecticGroup : Submonoid (Matrix (Sum l l) (Sum l l) R) where
-  carrier := { A | A ⬝ J l R ⬝ Aᵀ = J l R }
+  carrier := { A | A * J l R * Aᵀ = J l R }
   mul_mem' {a b} ha hb := by
-    simp only [mul_eq_mul, Set.mem_setOf_eq, transpose_mul] at *
+    simp only [Set.mem_setOf_eq, transpose_mul] at *
     rw [← Matrix.mul_assoc, a.mul_assoc, a.mul_assoc, hb]
     exact ha
   one_mem' := by simp
@@ -99,7 +99,7 @@ variable [DecidableEq l] [Fintype l] [CommRing R]
 open Matrix
 
 theorem mem_iff {A : Matrix (Sum l l) (Sum l l) R} :
-    A ∈ symplecticGroup l R ↔ A ⬝ J l R ⬝ Aᵀ = J l R := by simp [symplecticGroup]
+    A ∈ symplecticGroup l R ↔ A * J l R * Aᵀ = J l R := by simp [symplecticGroup]
 #align symplectic_group.mem_iff SymplecticGroup.mem_iff
 
 -- Porting note: Previous proof was `by infer_instance`
@@ -159,11 +159,11 @@ theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGrou
     rw [Matrix.det_transpose]
     exact huA
   calc
-    Aᵀ ⬝ J l R ⬝ A = (-Aᵀ) ⬝ (J l R)⁻¹ ⬝ A := by
+    Aᵀ * J l R * A = (-Aᵀ) * (J l R)⁻¹ * A := by
       rw [J_inv]
       simp
-    _ = (-Aᵀ) ⬝ (A ⬝ J l R ⬝ Aᵀ)⁻¹ ⬝ A := by rw [hA]
-    _ = (-Aᵀ ⬝ (Aᵀ⁻¹ ⬝ (J l R)⁻¹)) ⬝ A⁻¹ ⬝ A := by
+    _ = (-Aᵀ) * (A * J l R * Aᵀ)⁻¹ * A := by rw [hA]
+    _ = -(Aᵀ * (Aᵀ⁻¹ * (J l R)⁻¹)) * A⁻¹ * A := by
       simp only [Matrix.mul_inv_rev, Matrix.mul_assoc, Matrix.neg_mul]
     _ = -(J l R)⁻¹ := by
       rw [mul_nonsing_inv_cancel_left _ _ huAT, nonsing_inv_mul_cancel_right _ _ huA]
@@ -175,25 +175,25 @@ theorem transpose_mem_iff : Aᵀ ∈ symplecticGroup l R ↔ A ∈ symplecticGro
   ⟨fun hA => by simpa using transpose_mem hA, transpose_mem⟩
 #align symplectic_group.transpose_mem_iff SymplecticGroup.transpose_mem_iff
 
-theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ ⬝ J l R ⬝ A = J l R := by
+theorem mem_iff' : A ∈ symplecticGroup l R ↔ Aᵀ * J l R * A = J l R := by
   rw [← transpose_mem_iff, mem_iff, transpose_transpose]
 #align symplectic_group.mem_iff' SymplecticGroup.mem_iff'
 
 instance hasInv : Inv (symplecticGroup l R) where
-  inv A := ⟨(-J l R) ⬝ (A : Matrix (Sum l l) (Sum l l) R)ᵀ ⬝ J l R,
+  inv A := ⟨(-J l R) * (A : Matrix (Sum l l) (Sum l l) R)ᵀ * J l R,
       mul_mem (mul_mem (neg_mem <| J_mem _ _) <| transpose_mem A.2) <| J_mem _ _⟩
 
-theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) ⬝ (↑A)ᵀ ⬝ J l R := rfl
+theorem coe_inv (A : symplecticGroup l R) : (↑A⁻¹ : Matrix _ _ _) = (-J l R) * (↑A)ᵀ * J l R := rfl
 #align symplectic_group.coe_inv SymplecticGroup.coe_inv
 
-theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = 1 :=
+theorem inv_left_mul_aux (hA : A ∈ symplecticGroup l R) : -(J l R * Aᵀ * J l R * A) = 1 :=
   calc
-    -J l R ⬝ Aᵀ ⬝ J l R ⬝ A = (-J l R) ⬝ (Aᵀ ⬝ J l R ⬝ A) := by
+    -(J l R * Aᵀ * J l R * A) = (-J l R) * (Aᵀ * J l R * A) := by
       simp only [Matrix.mul_assoc, Matrix.neg_mul]
-    _ = (-J l R) ⬝ J l R := by
+    _ = (-J l R) * J l R := by
       rw [mem_iff'] at hA
       rw [hA]
-    _ = (-1 : R) • J l R ⬝ J l R := by simp only [Matrix.neg_mul, neg_smul, one_smul]
+    _ = (-1 : R) • (J l R * J l R) := by simp only [Matrix.neg_mul, neg_smul, one_smul]
     _ = (-1 : R) • (-1 : Matrix _ _ _) := by rw [J_squared]
     _ = 1 := by simp only [neg_smul_neg, one_smul]
 #align symplectic_group.inv_left_mul_aux SymplecticGroup.inv_left_mul_aux
@@ -204,7 +204,7 @@ theorem coe_inv' (A : symplecticGroup l R) : (↑A⁻¹ : Matrix (Sum l l) (Sum
 #align symplectic_group.coe_inv' SymplecticGroup.coe_inv'
 
 theorem inv_eq_symplectic_inv (A : Matrix (Sum l l) (Sum l l) R) (hA : A ∈ symplecticGroup l R) :
-    A⁻¹ = (-J l R) ⬝ Aᵀ ⬝ J l R :=
+    A⁻¹ = (-J l R) * Aᵀ * J l R :=
   inv_eq_left_inv (by simp only [Matrix.neg_mul, inv_left_mul_aux hA])
 #align symplectic_group.inv_eq_symplectic_inv SymplecticGroup.inv_eq_symplectic_inv
 
@@ -213,7 +213,6 @@ instance : Group (symplecticGroup l R) :=
     mul_left_inv := fun A => by
       apply Subtype.ext
       simp only [Submonoid.coe_one, Submonoid.coe_mul, Matrix.neg_mul, coe_inv]
-      rw [Matrix.mul_eq_mul, Matrix.neg_mul]
       exact inv_left_mul_aux A.2 }
 
 end SymplecticGroup

70fd9563

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

@@ -25,7 +25,7 @@ This file defines the symplectic group and proves elementary properties.
 
 open Matrix
 
-variable {l R : Type _}
+variable {l R : Type*}
 
 namespace Matrix

70fd9563

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) 2022 Matej Penciak. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Matej Penciak, Moritz Doll, Fabien Clery
-
-! This file was ported from Lean 3 source module linear_algebra.symplectic_group
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! 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.symplectic_group from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # The Symplectic Group

70fd9563

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

Changes are of the form

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

2a870323

Diff

@@ -138,7 +138,7 @@ end SymplecticJ
 variable {A : Matrix (Sum l l) (Sum l l) R}
 
 theorem neg_mem (h : A ∈ symplecticGroup l R) : -A ∈ symplecticGroup l R := by
-  rw [mem_iff] at h⊢
+  rw [mem_iff] at h ⊢
   simp [h]
 #align symplectic_group.neg_mem SymplecticGroup.neg_mem
 
@@ -155,7 +155,7 @@ theorem symplectic_det (hA : A ∈ symplecticGroup l R) : IsUnit <| det A := by
 #align symplectic_group.symplectic_det SymplecticGroup.symplectic_det
 
 theorem transpose_mem (hA : A ∈ symplecticGroup l R) : Aᵀ ∈ symplecticGroup l R := by
-  rw [mem_iff] at hA⊢
+  rw [mem_iff] at hA ⊢
   rw [transpose_transpose]
   have huA := symplectic_det hA
   have huAT : IsUnit Aᵀ.det := by

70fd9563

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

@@ -44,8 +44,8 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem J_transpose : (J l R)ᵀ = -J l R := by
-  rw [J, fromBlocks_transpose, ← neg_one_smul R (fromBlocks _ _ _ _), fromBlocks_smul,
-    Matrix.transpose_zero, Matrix.transpose_one, transpose_neg]
+  rw [J, fromBlocks_transpose, ← neg_one_smul R (fromBlocks _ _ _ _ : Matrix (l ⊕ l) (l ⊕ l) R),
+    fromBlocks_smul, Matrix.transpose_zero, Matrix.transpose_one, transpose_neg]
   simp [fromBlocks]
 set_option linter.uppercaseLean3 false in
 #align matrix.J_transpose Matrix.J_transpose

70fd9563

feat: port LinearAlgebra.SymplecticGroup (#3696)

27974dac

`linear_algebra.symplectic_group` ⟷ `Mathlib.LinearAlgebra.SymplecticGroup`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 573

linear_algebra.symplectic_group ⟷ Mathlib.LinearAlgebra.SymplecticGroup

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 573

`linear_algebra.symplectic_group` ⟷ `Mathlib.LinearAlgebra.SymplecticGroup`