algebra.lie.classical ⟷ Mathlib.Algebra.Lie.Classical

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Algebra.Invertible
+import Algebra.Invertible.Defs
 import Data.Matrix.Basis
-import Data.Matrix.Dmatrix
+import Data.Matrix.DMatrix
 import Algebra.Lie.Abelian
 import LinearAlgebra.Matrix.Trace
 import Algebra.Lie.SkewAdjoint

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

@@ -3,13 +3,13 @@ Copyright (c) 2020 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.Algebra.Invertible
-import Mathbin.Data.Matrix.Basis
-import Mathbin.Data.Matrix.Dmatrix
-import Mathbin.Algebra.Lie.Abelian
-import Mathbin.LinearAlgebra.Matrix.Trace
-import Mathbin.Algebra.Lie.SkewAdjoint
-import Mathbin.LinearAlgebra.SymplecticGroup
+import Algebra.Invertible
+import Data.Matrix.Basis
+import Data.Matrix.Dmatrix
+import Algebra.Lie.Abelian
+import LinearAlgebra.Matrix.Trace
+import Algebra.Lie.SkewAdjoint
+import LinearAlgebra.SymplecticGroup
 
 #align_import algebra.lie.classical from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -352,7 +352,7 @@ def typeDEquivSo' [Fintype l] [Invertible (2 : R)] : typeD l R ≃ₗ⁅R⁆ so'
   apply (skewAdjointMatricesLieSubalgebraEquiv (JD l R) (PD l R) (by infer_instance)).trans
   apply LieEquiv.ofEq
   ext A
-  rw [JD_transform, ← unitOfInvertible_val (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
+  rw [JD_transform, ← val_unitOfInvertible (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
     mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   rfl
 #align lie_algebra.orthogonal.type_D_equiv_so' LieAlgebra.Orthogonal.typeDEquivSo'
@@ -460,7 +460,7 @@ def typeBEquivSo' [Invertible (2 : R)] : typeB l R ≃ₗ⁅R⁆ so' (Sum Unit l
         (Matrix.reindexAlgEquiv _ (Equiv.sumAssoc PUnit l l)) (Matrix.transpose_reindex _ _)).trans
   apply LieEquiv.ofEq
   ext A
-  rw [JB_transform, ← unitOfInvertible_val (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
+  rw [JB_transform, ← val_unitOfInvertible (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
     LieSubalgebra.mem_coe, mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   simpa [indefinite_diagonal_assoc]
 #align lie_algebra.orthogonal.type_B_equiv_so' LieAlgebra.Orthogonal.typeBEquivSo'

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

@@ -333,7 +333,7 @@ theorem pd_inv [Fintype l] [Invertible (2 : R)] : PD l R * ⅟ (2 : R) • (PD l
   by
   have h : ⅟ (2 : R) • (1 : Matrix l l R) + ⅟ (2 : R) • 1 = 1 := by
     rw [← smul_add, ← two_smul R _, smul_smul, invOf_mul_self, one_smul]
-  erw [Matrix.fromBlocks_transpose, Matrix.fromBlocks_smul, Matrix.mul_eq_mul,
+  erw [Matrix.fromBlocks_transpose, Matrix.fromBlocks_smul, Matrix.hMul_eq_hMul,
     Matrix.fromBlocks_multiply]
   simp [h]
 #align lie_algebra.orthogonal.PD_inv LieAlgebra.Orthogonal.pd_inv
@@ -412,7 +412,7 @@ variable [Fintype l]
 #print LieAlgebra.Orthogonal.pb_inv /-
 theorem pb_inv [Invertible (2 : R)] : PB l R * Matrix.fromBlocks 1 0 0 (⅟ (PD l R)) = 1 :=
   by
-  rw [PB, Matrix.mul_eq_mul, Matrix.fromBlocks_multiply, Matrix.mul_invOf_self]
+  rw [PB, Matrix.hMul_eq_hMul, Matrix.fromBlocks_multiply, mul_invOf_self]
   simp only [Matrix.mul_zero, Matrix.mul_one, Matrix.zero_mul, zero_add, add_zero,
     Matrix.fromBlocks_one]
 #align lie_algebra.orthogonal.PB_inv LieAlgebra.Orthogonal.pb_inv

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.classical
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Invertible
 import Mathbin.Data.Matrix.Basis
@@ -16,6 +11,8 @@ import Mathbin.LinearAlgebra.Matrix.Trace
 import Mathbin.Algebra.Lie.SkewAdjoint
 import Mathbin.LinearAlgebra.SymplecticGroup
 
+#align_import algebra.lie.classical from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Classical Lie algebras
 

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

@@ -211,7 +211,7 @@ variable [Fintype p] [Fintype q]
 #print LieAlgebra.Orthogonal.pso_inv /-
 theorem pso_inv {i : R} (hi : i * i = -1) : Pso p q R i * Pso p q R (-i) = 1 :=
   by
-  ext (x y); rcases x with ⟨⟩ <;> rcases y with ⟨⟩
+  ext x y; rcases x with ⟨⟩ <;> rcases y with ⟨⟩
   ·-- x y : p
       by_cases h : x = y <;>
       simp [Pso, indefinite_diagonal, h]
@@ -236,7 +236,7 @@ def invertiblePso {i : R} (hi : i * i = -1) : Invertible (Pso p q R i) :=
 theorem indefiniteDiagonal_transform {i : R} (hi : i * i = -1) :
     (Pso p q R i)ᵀ ⬝ indefiniteDiagonal p q R ⬝ Pso p q R i = 1 :=
   by
-  ext (x y); rcases x with ⟨⟩ <;> rcases y with ⟨⟩
+  ext x y; rcases x with ⟨⟩ <;> rcases y with ⟨⟩
   ·-- x y : p
       by_cases h : x = y <;>
       simp [Pso, indefinite_diagonal, h]
@@ -440,7 +440,7 @@ theorem indefiniteDiagonal_assoc :
       Matrix.reindexLieEquiv (Equiv.sumAssoc Unit l l).symm
         (Matrix.fromBlocks 1 0 0 (indefiniteDiagonal l l R)) :=
   by
-  ext (i j)
+  ext i j
   rcases i with ⟨⟨i₁ | i₂⟩ | i₃⟩ <;> rcases j with ⟨⟨j₁ | j₂⟩ | j₃⟩ <;>
       simp only [indefinite_diagonal, Matrix.diagonal_apply, Equiv.sumAssoc_apply_inl_inl,
         Matrix.reindexLieEquiv_apply, Matrix.submatrix_apply, Equiv.symm_symm, Matrix.reindex_apply,

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

@@ -87,6 +87,7 @@ variable [DecidableEq n] [DecidableEq p] [DecidableEq q] [DecidableEq l]
 
 variable [CommRing R]
 
+#print LieAlgebra.matrix_trace_commutator_zero /-
 @[simp]
 theorem matrix_trace_commutator_zero [Fintype n] (X Y : Matrix n n R) : Matrix.trace ⁅X, Y⁆ = 0 :=
   calc
@@ -95,18 +96,23 @@ theorem matrix_trace_commutator_zero [Fintype n] (X Y : Matrix n n R) : Matrix.t
       (congr_arg (fun x => _ - x) (Matrix.trace_mul_comm Y X))
     _ = 0 := sub_self _
 #align lie_algebra.matrix_trace_commutator_zero LieAlgebra.matrix_trace_commutator_zero
+-/
 
 namespace SpecialLinear
 
+#print LieAlgebra.SpecialLinear.sl /-
 /-- The special linear Lie algebra: square matrices of trace zero. -/
 def sl [Fintype n] : LieSubalgebra R (Matrix n n R) :=
   { LinearMap.ker (Matrix.traceLinearMap n R R) with
     lie_mem' := fun X Y _ _ => LinearMap.mem_ker.2 <| matrix_trace_commutator_zero _ _ _ _ }
 #align lie_algebra.special_linear.sl LieAlgebra.SpecialLinear.sl
+-/
 
+#print LieAlgebra.SpecialLinear.sl_bracket /-
 theorem sl_bracket [Fintype n] (A B : sl n R) : ⁅A, B⁆.val = A.val ⬝ B.val - B.val ⬝ A.val :=
   rfl
 #align lie_algebra.special_linear.sl_bracket LieAlgebra.SpecialLinear.sl_bracket
+-/
 
 section ElementaryBasis
 
@@ -122,13 +128,16 @@ def Eb (h : j ≠ i) : sl n R :=
 #align lie_algebra.special_linear.Eb LieAlgebra.SpecialLinear.Eb
 -/
 
+#print LieAlgebra.SpecialLinear.eb_val /-
 @[simp]
 theorem eb_val (h : j ≠ i) : (Eb R i j h).val = Matrix.stdBasisMatrix i j 1 :=
   rfl
 #align lie_algebra.special_linear.Eb_val LieAlgebra.SpecialLinear.eb_val
+-/
 
 end ElementaryBasis
 
+#print LieAlgebra.SpecialLinear.sl_non_abelian /-
 theorem sl_non_abelian [Fintype n] [Nontrivial R] (h : 1 < Fintype.card n) :
     ¬IsLieAbelian ↥(sl n R) :=
   by
@@ -139,33 +148,40 @@ theorem sl_non_abelian [Fintype n] [Nontrivial R] (h : 1 < Fintype.card n) :
   have c' : A.val ⬝ B.val = B.val ⬝ A.val := by rw [← sub_eq_zero, ← sl_bracket, c.trivial]; rfl
   simpa [std_basis_matrix, Matrix.mul_apply, hij] using congr_fun (congr_fun c' i) i
 #align lie_algebra.special_linear.sl_non_abelian LieAlgebra.SpecialLinear.sl_non_abelian
+-/
 
 end SpecialLinear
 
 namespace Symplectic
 
+#print LieAlgebra.Symplectic.sp /-
 /-- The symplectic Lie algebra: skew-adjoint matrices with respect to the canonical skew-symmetric
 bilinear form. -/
 def sp [Fintype l] : LieSubalgebra R (Matrix (Sum l l) (Sum l l) R) :=
   skewAdjointMatricesLieSubalgebra (Matrix.J l R)
 #align lie_algebra.symplectic.sp LieAlgebra.Symplectic.sp
+-/
 
 end Symplectic
 
 namespace Orthogonal
 
+#print LieAlgebra.Orthogonal.so /-
 /-- The definite orthogonal Lie subalgebra: skew-adjoint matrices with respect to the symmetric
 bilinear form defined by the identity matrix. -/
 def so [Fintype n] : LieSubalgebra R (Matrix n n R) :=
   skewAdjointMatricesLieSubalgebra (1 : Matrix n n R)
 #align lie_algebra.orthogonal.so LieAlgebra.Orthogonal.so
+-/
 
+#print LieAlgebra.Orthogonal.mem_so /-
 @[simp]
 theorem mem_so [Fintype n] (A : Matrix n n R) : A ∈ so n R ↔ Aᵀ = -A :=
   by
   erw [mem_skewAdjointMatricesSubmodule]
   simp only [Matrix.IsSkewAdjoint, Matrix.IsAdjointPair, Matrix.mul_one, Matrix.one_mul]
 #align lie_algebra.orthogonal.mem_so LieAlgebra.Orthogonal.mem_so
+-/
 
 #print LieAlgebra.Orthogonal.indefiniteDiagonal /-
 /-- The indefinite diagonal matrix with `p` 1s and `q` -1s. -/
@@ -174,11 +190,13 @@ def indefiniteDiagonal : Matrix (Sum p q) (Sum p q) R :=
 #align lie_algebra.orthogonal.indefinite_diagonal LieAlgebra.Orthogonal.indefiniteDiagonal
 -/
 
+#print LieAlgebra.Orthogonal.so' /-
 /-- The indefinite orthogonal Lie subalgebra: skew-adjoint matrices with respect to the symmetric
 bilinear form defined by the indefinite diagonal matrix. -/
 def so' [Fintype p] [Fintype q] : LieSubalgebra R (Matrix (Sum p q) (Sum p q) R) :=
   skewAdjointMatricesLieSubalgebra <| indefiniteDiagonal p q R
 #align lie_algebra.orthogonal.so' LieAlgebra.Orthogonal.so'
+-/
 
 #print LieAlgebra.Orthogonal.Pso /-
 /-- A matrix for transforming the indefinite diagonal bilinear form into the definite one, provided
@@ -190,6 +208,7 @@ def Pso (i : R) : Matrix (Sum p q) (Sum p q) R :=
 
 variable [Fintype p] [Fintype q]
 
+#print LieAlgebra.Orthogonal.pso_inv /-
 theorem pso_inv {i : R} (hi : i * i = -1) : Pso p q R i * Pso p q R (-i) = 1 :=
   by
   ext (x y); rcases x with ⟨⟩ <;> rcases y with ⟨⟩
@@ -204,12 +223,16 @@ theorem pso_inv {i : R} (hi : i * i = -1) : Pso p q R i * Pso p q R (-i) = 1 :=
       by_cases h : x = y <;>
       simp [Pso, indefinite_diagonal, h, hi]
 #align lie_algebra.orthogonal.Pso_inv LieAlgebra.Orthogonal.pso_inv
+-/
 
+#print LieAlgebra.Orthogonal.invertiblePso /-
 /-- There is a constructive inverse of `Pso p q R i`. -/
 def invertiblePso {i : R} (hi : i * i = -1) : Invertible (Pso p q R i) :=
   invertibleOfRightInverse _ _ (pso_inv p q R hi)
 #align lie_algebra.orthogonal.invertible_Pso LieAlgebra.Orthogonal.invertiblePso
+-/
 
+#print LieAlgebra.Orthogonal.indefiniteDiagonal_transform /-
 theorem indefiniteDiagonal_transform {i : R} (hi : i * i = -1) :
     (Pso p q R i)ᵀ ⬝ indefiniteDiagonal p q R ⬝ Pso p q R i = 1 :=
   by
@@ -225,7 +248,9 @@ theorem indefiniteDiagonal_transform {i : R} (hi : i * i = -1) :
       by_cases h : x = y <;>
       simp [Pso, indefinite_diagonal, h, hi]
 #align lie_algebra.orthogonal.indefinite_diagonal_transform LieAlgebra.Orthogonal.indefiniteDiagonal_transform
+-/
 
+#print LieAlgebra.Orthogonal.soIndefiniteEquiv /-
 /-- An equivalence between the indefinite and definite orthogonal Lie algebras, over a ring
 containing a square root of -1. -/
 def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Sum p q) R :=
@@ -236,12 +261,15 @@ def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Su
   apply LieEquiv.ofEq
   ext A; rw [indefinite_diagonal_transform p q R hi]; rfl
 #align lie_algebra.orthogonal.so_indefinite_equiv LieAlgebra.Orthogonal.soIndefiniteEquiv
+-/
 
+#print LieAlgebra.Orthogonal.soIndefiniteEquiv_apply /-
 theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (Sum p q) (Sum p q) R) =
       (Pso p q R i)⁻¹ ⬝ (A : Matrix (Sum p q) (Sum p q) R) ⬝ Pso p q R i :=
   by erw [LieEquiv.trans_apply, LieEquiv.ofEq_apply, skewAdjointMatricesLieSubalgebraEquiv_apply]
 #align lie_algebra.orthogonal.so_indefinite_equiv_apply LieAlgebra.Orthogonal.soIndefiniteEquiv_apply
+-/
 
 #print LieAlgebra.Orthogonal.JD /-
 /-- A matrix defining a canonical even-rank symmetric bilinear form.
@@ -256,11 +284,13 @@ def JD : Matrix (Sum l l) (Sum l l) R :=
 #align lie_algebra.orthogonal.JD LieAlgebra.Orthogonal.JD
 -/
 
+#print LieAlgebra.Orthogonal.typeD /-
 /-- The classical Lie algebra of type D as a Lie subalgebra of matrices associated to the matrix
 `JD`. -/
 def typeD [Fintype l] :=
   skewAdjointMatricesLieSubalgebra (JD l R)
 #align lie_algebra.orthogonal.type_D LieAlgebra.Orthogonal.typeD
+-/
 
 #print LieAlgebra.Orthogonal.PD /-
 /-- A matrix transforming the bilinear form defined by the matrix `JD` into a split-signature
@@ -283,12 +313,15 @@ def S :=
 #align lie_algebra.orthogonal.S LieAlgebra.Orthogonal.S
 -/
 
+#print LieAlgebra.Orthogonal.s_as_blocks /-
 theorem s_as_blocks : S l R = Matrix.fromBlocks 1 0 0 (-1) :=
   by
   rw [← Matrix.diagonal_one, Matrix.diagonal_neg, Matrix.fromBlocks_diagonal]
   rfl
 #align lie_algebra.orthogonal.S_as_blocks LieAlgebra.Orthogonal.s_as_blocks
+-/
 
+#print LieAlgebra.Orthogonal.jd_transform /-
 theorem jd_transform [Fintype l] : (PD l R)ᵀ ⬝ JD l R ⬝ PD l R = (2 : R) • S l R :=
   by
   have h : (PD l R)ᵀ ⬝ JD l R = Matrix.fromBlocks 1 1 1 (-1) := by
@@ -296,7 +329,9 @@ theorem jd_transform [Fintype l] : (PD l R)ᵀ ⬝ JD l R ⬝ PD l R = (2 : R) 
   erw [h, S_as_blocks, Matrix.fromBlocks_multiply, Matrix.fromBlocks_smul]
   congr <;> simp [two_smul]
 #align lie_algebra.orthogonal.JD_transform LieAlgebra.Orthogonal.jd_transform
+-/
 
+#print LieAlgebra.Orthogonal.pd_inv /-
 theorem pd_inv [Fintype l] [Invertible (2 : R)] : PD l R * ⅟ (2 : R) • (PD l R)ᵀ = 1 :=
   by
   have h : ⅟ (2 : R) • (1 : Matrix l l R) + ⅟ (2 : R) • 1 = 1 := by
@@ -305,11 +340,15 @@ theorem pd_inv [Fintype l] [Invertible (2 : R)] : PD l R * ⅟ (2 : R) • (PD l
     Matrix.fromBlocks_multiply]
   simp [h]
 #align lie_algebra.orthogonal.PD_inv LieAlgebra.Orthogonal.pd_inv
+-/
 
+#print LieAlgebra.Orthogonal.invertiblePD /-
 instance invertiblePD [Fintype l] [Invertible (2 : R)] : Invertible (PD l R) :=
   invertibleOfRightInverse _ _ (pd_inv l R)
 #align lie_algebra.orthogonal.invertible_PD LieAlgebra.Orthogonal.invertiblePD
+-/
 
+#print LieAlgebra.Orthogonal.typeDEquivSo' /-
 /-- An equivalence between two possible definitions of the classical Lie algebra of type D. -/
 def typeDEquivSo' [Fintype l] [Invertible (2 : R)] : typeD l R ≃ₗ⁅R⁆ so' l l R :=
   by
@@ -320,6 +359,7 @@ def typeDEquivSo' [Fintype l] [Invertible (2 : R)] : typeD l R ≃ₗ⁅R⁆ so'
     mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   rfl
 #align lie_algebra.orthogonal.type_D_equiv_so' LieAlgebra.Orthogonal.typeDEquivSo'
+-/
 
 #print LieAlgebra.Orthogonal.JB /-
 /-- A matrix defining a canonical odd-rank symmetric bilinear form.
@@ -341,11 +381,13 @@ def JB :=
 #align lie_algebra.orthogonal.JB LieAlgebra.Orthogonal.JB
 -/
 
+#print LieAlgebra.Orthogonal.typeB /-
 /-- The classical Lie algebra of type B as a Lie subalgebra of matrices associated to the matrix
 `JB`. -/
 def typeB [Fintype l] :=
   skewAdjointMatricesLieSubalgebra (JB l R)
 #align lie_algebra.orthogonal.type_B LieAlgebra.Orthogonal.typeB
+-/
 
 #print LieAlgebra.Orthogonal.PB /-
 /-- A matrix transforming the bilinear form defined by the matrix `JB` into an
@@ -370,22 +412,29 @@ def PB :=
 
 variable [Fintype l]
 
+#print LieAlgebra.Orthogonal.pb_inv /-
 theorem pb_inv [Invertible (2 : R)] : PB l R * Matrix.fromBlocks 1 0 0 (⅟ (PD l R)) = 1 :=
   by
   rw [PB, Matrix.mul_eq_mul, Matrix.fromBlocks_multiply, Matrix.mul_invOf_self]
   simp only [Matrix.mul_zero, Matrix.mul_one, Matrix.zero_mul, zero_add, add_zero,
     Matrix.fromBlocks_one]
 #align lie_algebra.orthogonal.PB_inv LieAlgebra.Orthogonal.pb_inv
+-/
 
+#print LieAlgebra.Orthogonal.invertiblePB /-
 instance invertiblePB [Invertible (2 : R)] : Invertible (PB l R) :=
   invertibleOfRightInverse _ _ (pb_inv l R)
 #align lie_algebra.orthogonal.invertible_PB LieAlgebra.Orthogonal.invertiblePB
+-/
 
+#print LieAlgebra.Orthogonal.jb_transform /-
 theorem jb_transform : (PB l R)ᵀ ⬝ JB l R ⬝ PB l R = (2 : R) • Matrix.fromBlocks 1 0 0 (S l R) := by
   simp [PB, JB, JD_transform, Matrix.fromBlocks_transpose, Matrix.fromBlocks_multiply,
     Matrix.fromBlocks_smul]
 #align lie_algebra.orthogonal.JB_transform LieAlgebra.Orthogonal.jb_transform
+-/
 
+#print LieAlgebra.Orthogonal.indefiniteDiagonal_assoc /-
 theorem indefiniteDiagonal_assoc :
     indefiniteDiagonal (Sum Unit l) l R =
       Matrix.reindexLieEquiv (Equiv.sumAssoc Unit l l).symm
@@ -401,7 +450,9 @@ theorem indefiniteDiagonal_assoc :
         Sum.elim_inr] <;>
     congr
 #align lie_algebra.orthogonal.indefinite_diagonal_assoc LieAlgebra.Orthogonal.indefiniteDiagonal_assoc
+-/
 
+#print LieAlgebra.Orthogonal.typeBEquivSo' /-
 /-- An equivalence between two possible definitions of the classical Lie algebra of type B. -/
 def typeBEquivSo' [Invertible (2 : R)] : typeB l R ≃ₗ⁅R⁆ so' (Sum Unit l) l R :=
   by
@@ -416,6 +467,7 @@ def typeBEquivSo' [Invertible (2 : R)] : typeB l R ≃ₗ⁅R⁆ so' (Sum Unit l
     LieSubalgebra.mem_coe, mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   simpa [indefinite_diagonal_assoc]
 #align lie_algebra.orthogonal.type_B_equiv_so' LieAlgebra.Orthogonal.typeBEquivSo'
+-/
 
 end Orthogonal
 

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

@@ -94,7 +94,6 @@ theorem matrix_trace_commutator_zero [Fintype n] (X Y : Matrix n n R) : Matrix.t
     _ = Matrix.trace (X ⬝ Y) - Matrix.trace (X ⬝ Y) :=
       (congr_arg (fun x => _ - x) (Matrix.trace_mul_comm Y X))
     _ = 0 := sub_self _
-    
 #align lie_algebra.matrix_trace_commutator_zero LieAlgebra.matrix_trace_commutator_zero
 
 namespace SpecialLinear

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module algebra.lie.classical
-! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.LinearAlgebra.SymplecticGroup
 /-!
 # Classical Lie algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file is the place to find definitions and basic properties of the classical Lie algebras:
   * Aₗ = sl(l+1)
   * Bₗ ≃ so(l+1, l) ≃ so(2l+1)

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

@@ -110,16 +110,18 @@ section ElementaryBasis
 
 variable {n} [Fintype n] (i j : n)
 
+#print LieAlgebra.SpecialLinear.Eb /-
 /-- When j ≠ i, the elementary matrices are elements of sl n R, in fact they are part of a natural
 basis of sl n R. -/
-def eb (h : j ≠ i) : sl n R :=
+def Eb (h : j ≠ i) : sl n R :=
   ⟨Matrix.stdBasisMatrix i j (1 : R),
     show Matrix.stdBasisMatrix i j (1 : R) ∈ LinearMap.ker (Matrix.traceLinearMap n R R) from
       Matrix.StdBasisMatrix.trace_zero i j (1 : R) h⟩
-#align lie_algebra.special_linear.Eb LieAlgebra.SpecialLinear.eb
+#align lie_algebra.special_linear.Eb LieAlgebra.SpecialLinear.Eb
+-/
 
 @[simp]
-theorem eb_val (h : j ≠ i) : (eb R i j h).val = Matrix.stdBasisMatrix i j 1 :=
+theorem eb_val (h : j ≠ i) : (Eb R i j h).val = Matrix.stdBasisMatrix i j 1 :=
   rfl
 #align lie_algebra.special_linear.Eb_val LieAlgebra.SpecialLinear.eb_val
 
@@ -163,10 +165,12 @@ theorem mem_so [Fintype n] (A : Matrix n n R) : A ∈ so n R ↔ Aᵀ = -A :=
   simp only [Matrix.IsSkewAdjoint, Matrix.IsAdjointPair, Matrix.mul_one, Matrix.one_mul]
 #align lie_algebra.orthogonal.mem_so LieAlgebra.Orthogonal.mem_so
 
+#print LieAlgebra.Orthogonal.indefiniteDiagonal /-
 /-- The indefinite diagonal matrix with `p` 1s and `q` -1s. -/
 def indefiniteDiagonal : Matrix (Sum p q) (Sum p q) R :=
   Matrix.diagonal <| Sum.elim (fun _ => 1) fun _ => -1
 #align lie_algebra.orthogonal.indefinite_diagonal LieAlgebra.Orthogonal.indefiniteDiagonal
+-/
 
 /-- The indefinite orthogonal Lie subalgebra: skew-adjoint matrices with respect to the symmetric
 bilinear form defined by the indefinite diagonal matrix. -/
@@ -174,15 +178,17 @@ def so' [Fintype p] [Fintype q] : LieSubalgebra R (Matrix (Sum p q) (Sum p q) R)
   skewAdjointMatricesLieSubalgebra <| indefiniteDiagonal p q R
 #align lie_algebra.orthogonal.so' LieAlgebra.Orthogonal.so'
 
+#print LieAlgebra.Orthogonal.Pso /-
 /-- A matrix for transforming the indefinite diagonal bilinear form into the definite one, provided
 the parameter `i` is a square root of -1. -/
-def pso (i : R) : Matrix (Sum p q) (Sum p q) R :=
+def Pso (i : R) : Matrix (Sum p q) (Sum p q) R :=
   Matrix.diagonal <| Sum.elim (fun _ => 1) fun _ => i
-#align lie_algebra.orthogonal.Pso LieAlgebra.Orthogonal.pso
+#align lie_algebra.orthogonal.Pso LieAlgebra.Orthogonal.Pso
+-/
 
 variable [Fintype p] [Fintype q]
 
-theorem pso_inv {i : R} (hi : i * i = -1) : pso p q R i * pso p q R (-i) = 1 :=
+theorem pso_inv {i : R} (hi : i * i = -1) : Pso p q R i * Pso p q R (-i) = 1 :=
   by
   ext (x y); rcases x with ⟨⟩ <;> rcases y with ⟨⟩
   ·-- x y : p
@@ -198,12 +204,12 @@ theorem pso_inv {i : R} (hi : i * i = -1) : pso p q R i * pso p q R (-i) = 1 :=
 #align lie_algebra.orthogonal.Pso_inv LieAlgebra.Orthogonal.pso_inv
 
 /-- There is a constructive inverse of `Pso p q R i`. -/
-def invertiblePso {i : R} (hi : i * i = -1) : Invertible (pso p q R i) :=
+def invertiblePso {i : R} (hi : i * i = -1) : Invertible (Pso p q R i) :=
   invertibleOfRightInverse _ _ (pso_inv p q R hi)
 #align lie_algebra.orthogonal.invertible_Pso LieAlgebra.Orthogonal.invertiblePso
 
 theorem indefiniteDiagonal_transform {i : R} (hi : i * i = -1) :
-    (pso p q R i)ᵀ ⬝ indefiniteDiagonal p q R ⬝ pso p q R i = 1 :=
+    (Pso p q R i)ᵀ ⬝ indefiniteDiagonal p q R ⬝ Pso p q R i = 1 :=
   by
   ext (x y); rcases x with ⟨⟩ <;> rcases y with ⟨⟩
   ·-- x y : p
@@ -231,10 +237,11 @@ def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Su
 
 theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (Sum p q) (Sum p q) R) =
-      (pso p q R i)⁻¹ ⬝ (A : Matrix (Sum p q) (Sum p q) R) ⬝ pso p q R i :=
+      (Pso p q R i)⁻¹ ⬝ (A : Matrix (Sum p q) (Sum p q) R) ⬝ Pso p q R i :=
   by erw [LieEquiv.trans_apply, LieEquiv.ofEq_apply, skewAdjointMatricesLieSubalgebraEquiv_apply]
 #align lie_algebra.orthogonal.so_indefinite_equiv_apply LieAlgebra.Orthogonal.soIndefiniteEquiv_apply
 
+#print LieAlgebra.Orthogonal.JD /-
 /-- A matrix defining a canonical even-rank symmetric bilinear form.
 
 It looks like this as a `2l x 2l` matrix of `l x l` blocks:
@@ -242,16 +249,18 @@ It looks like this as a `2l x 2l` matrix of `l x l` blocks:
    [ 0 1 ]
    [ 1 0 ]
 -/
-def jD : Matrix (Sum l l) (Sum l l) R :=
+def JD : Matrix (Sum l l) (Sum l l) R :=
   Matrix.fromBlocks 0 1 1 0
-#align lie_algebra.orthogonal.JD LieAlgebra.Orthogonal.jD
+#align lie_algebra.orthogonal.JD LieAlgebra.Orthogonal.JD
+-/
 
 /-- The classical Lie algebra of type D as a Lie subalgebra of matrices associated to the matrix
 `JD`. -/
 def typeD [Fintype l] :=
-  skewAdjointMatricesLieSubalgebra (jD l R)
+  skewAdjointMatricesLieSubalgebra (JD l R)
 #align lie_algebra.orthogonal.type_D LieAlgebra.Orthogonal.typeD
 
+#print LieAlgebra.Orthogonal.PD /-
 /-- A matrix transforming the bilinear form defined by the matrix `JD` into a split-signature
 diagonal matrix.
 
@@ -260,40 +269,43 @@ It looks like this as a `2l x 2l` matrix of `l x l` blocks:
    [ 1 -1 ]
    [ 1  1 ]
 -/
-def pD : Matrix (Sum l l) (Sum l l) R :=
+def PD : Matrix (Sum l l) (Sum l l) R :=
   Matrix.fromBlocks 1 (-1) 1 1
-#align lie_algebra.orthogonal.PD LieAlgebra.Orthogonal.pD
+#align lie_algebra.orthogonal.PD LieAlgebra.Orthogonal.PD
+-/
 
+#print LieAlgebra.Orthogonal.S /-
 /-- The split-signature diagonal matrix. -/
-def s :=
+def S :=
   indefiniteDiagonal l l R
-#align lie_algebra.orthogonal.S LieAlgebra.Orthogonal.s
+#align lie_algebra.orthogonal.S LieAlgebra.Orthogonal.S
+-/
 
-theorem s_as_blocks : s l R = Matrix.fromBlocks 1 0 0 (-1) :=
+theorem s_as_blocks : S l R = Matrix.fromBlocks 1 0 0 (-1) :=
   by
   rw [← Matrix.diagonal_one, Matrix.diagonal_neg, Matrix.fromBlocks_diagonal]
   rfl
 #align lie_algebra.orthogonal.S_as_blocks LieAlgebra.Orthogonal.s_as_blocks
 
-theorem jD_transform [Fintype l] : (pD l R)ᵀ ⬝ jD l R ⬝ pD l R = (2 : R) • s l R :=
+theorem jd_transform [Fintype l] : (PD l R)ᵀ ⬝ JD l R ⬝ PD l R = (2 : R) • S l R :=
   by
   have h : (PD l R)ᵀ ⬝ JD l R = Matrix.fromBlocks 1 1 1 (-1) := by
     simp [PD, JD, Matrix.fromBlocks_transpose, Matrix.fromBlocks_multiply]
   erw [h, S_as_blocks, Matrix.fromBlocks_multiply, Matrix.fromBlocks_smul]
   congr <;> simp [two_smul]
-#align lie_algebra.orthogonal.JD_transform LieAlgebra.Orthogonal.jD_transform
+#align lie_algebra.orthogonal.JD_transform LieAlgebra.Orthogonal.jd_transform
 
-theorem pD_inv [Fintype l] [Invertible (2 : R)] : pD l R * ⅟ (2 : R) • (pD l R)ᵀ = 1 :=
+theorem pd_inv [Fintype l] [Invertible (2 : R)] : PD l R * ⅟ (2 : R) • (PD l R)ᵀ = 1 :=
   by
   have h : ⅟ (2 : R) • (1 : Matrix l l R) + ⅟ (2 : R) • 1 = 1 := by
     rw [← smul_add, ← two_smul R _, smul_smul, invOf_mul_self, one_smul]
   erw [Matrix.fromBlocks_transpose, Matrix.fromBlocks_smul, Matrix.mul_eq_mul,
     Matrix.fromBlocks_multiply]
   simp [h]
-#align lie_algebra.orthogonal.PD_inv LieAlgebra.Orthogonal.pD_inv
+#align lie_algebra.orthogonal.PD_inv LieAlgebra.Orthogonal.pd_inv
 
-instance invertiblePD [Fintype l] [Invertible (2 : R)] : Invertible (pD l R) :=
-  invertibleOfRightInverse _ _ (pD_inv l R)
+instance invertiblePD [Fintype l] [Invertible (2 : R)] : Invertible (PD l R) :=
+  invertibleOfRightInverse _ _ (pd_inv l R)
 #align lie_algebra.orthogonal.invertible_PD LieAlgebra.Orthogonal.invertiblePD
 
 /-- An equivalence between two possible definitions of the classical Lie algebra of type D. -/
@@ -302,11 +314,12 @@ def typeDEquivSo' [Fintype l] [Invertible (2 : R)] : typeD l R ≃ₗ⁅R⁆ so'
   apply (skewAdjointMatricesLieSubalgebraEquiv (JD l R) (PD l R) (by infer_instance)).trans
   apply LieEquiv.ofEq
   ext A
-  rw [JD_transform, ← coe_unitOfInvertible (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
+  rw [JD_transform, ← unitOfInvertible_val (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
     mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   rfl
 #align lie_algebra.orthogonal.type_D_equiv_so' LieAlgebra.Orthogonal.typeDEquivSo'
 
+#print LieAlgebra.Orthogonal.JB /-
 /-- A matrix defining a canonical odd-rank symmetric bilinear form.
 
 It looks like this as a `(2l+1) x (2l+1)` matrix of blocks:
@@ -321,16 +334,18 @@ where sizes of the blocks are:
    [`l x 1` `l x l` `l x l`]
    [`l x 1` `l x l` `l x l`]
 -/
-def jB :=
-  Matrix.fromBlocks ((2 : R) • 1 : Matrix Unit Unit R) 0 0 (jD l R)
-#align lie_algebra.orthogonal.JB LieAlgebra.Orthogonal.jB
+def JB :=
+  Matrix.fromBlocks ((2 : R) • 1 : Matrix Unit Unit R) 0 0 (JD l R)
+#align lie_algebra.orthogonal.JB LieAlgebra.Orthogonal.JB
+-/
 
 /-- The classical Lie algebra of type B as a Lie subalgebra of matrices associated to the matrix
 `JB`. -/
 def typeB [Fintype l] :=
-  skewAdjointMatricesLieSubalgebra (jB l R)
+  skewAdjointMatricesLieSubalgebra (JB l R)
 #align lie_algebra.orthogonal.type_B LieAlgebra.Orthogonal.typeB
 
+#print LieAlgebra.Orthogonal.PB /-
 /-- A matrix transforming the bilinear form defined by the matrix `JB` into an
 almost-split-signature diagonal matrix.
 
@@ -346,27 +361,28 @@ where sizes of the blocks are:
    [`l x 1` `l x l` `l x l`]
    [`l x 1` `l x l` `l x l`]
 -/
-def pB :=
-  Matrix.fromBlocks (1 : Matrix Unit Unit R) 0 0 (pD l R)
-#align lie_algebra.orthogonal.PB LieAlgebra.Orthogonal.pB
+def PB :=
+  Matrix.fromBlocks (1 : Matrix Unit Unit R) 0 0 (PD l R)
+#align lie_algebra.orthogonal.PB LieAlgebra.Orthogonal.PB
+-/
 
 variable [Fintype l]
 
-theorem pB_inv [Invertible (2 : R)] : pB l R * Matrix.fromBlocks 1 0 0 (⅟ (pD l R)) = 1 :=
+theorem pb_inv [Invertible (2 : R)] : PB l R * Matrix.fromBlocks 1 0 0 (⅟ (PD l R)) = 1 :=
   by
   rw [PB, Matrix.mul_eq_mul, Matrix.fromBlocks_multiply, Matrix.mul_invOf_self]
   simp only [Matrix.mul_zero, Matrix.mul_one, Matrix.zero_mul, zero_add, add_zero,
     Matrix.fromBlocks_one]
-#align lie_algebra.orthogonal.PB_inv LieAlgebra.Orthogonal.pB_inv
+#align lie_algebra.orthogonal.PB_inv LieAlgebra.Orthogonal.pb_inv
 
-instance invertiblePB [Invertible (2 : R)] : Invertible (pB l R) :=
-  invertibleOfRightInverse _ _ (pB_inv l R)
+instance invertiblePB [Invertible (2 : R)] : Invertible (PB l R) :=
+  invertibleOfRightInverse _ _ (pb_inv l R)
 #align lie_algebra.orthogonal.invertible_PB LieAlgebra.Orthogonal.invertiblePB
 
-theorem jB_transform : (pB l R)ᵀ ⬝ jB l R ⬝ pB l R = (2 : R) • Matrix.fromBlocks 1 0 0 (s l R) := by
+theorem jb_transform : (PB l R)ᵀ ⬝ JB l R ⬝ PB l R = (2 : R) • Matrix.fromBlocks 1 0 0 (S l R) := by
   simp [PB, JB, JD_transform, Matrix.fromBlocks_transpose, Matrix.fromBlocks_multiply,
     Matrix.fromBlocks_smul]
-#align lie_algebra.orthogonal.JB_transform LieAlgebra.Orthogonal.jB_transform
+#align lie_algebra.orthogonal.JB_transform LieAlgebra.Orthogonal.jb_transform
 
 theorem indefiniteDiagonal_assoc :
     indefiniteDiagonal (Sum Unit l) l R =
@@ -394,7 +410,7 @@ def typeBEquivSo' [Invertible (2 : R)] : typeB l R ≃ₗ⁅R⁆ so' (Sum Unit l
         (Matrix.reindexAlgEquiv _ (Equiv.sumAssoc PUnit l l)) (Matrix.transpose_reindex _ _)).trans
   apply LieEquiv.ofEq
   ext A
-  rw [JB_transform, ← coe_unitOfInvertible (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
+  rw [JB_transform, ← unitOfInvertible_val (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
     LieSubalgebra.mem_coe, mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   simpa [indefinite_diagonal_assoc]
 #align lie_algebra.orthogonal.type_B_equiv_so' LieAlgebra.Orthogonal.typeBEquivSo'

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

@@ -76,7 +76,7 @@ namespace LieAlgebra
 
 open Matrix
 
-open Matrix
+open scoped Matrix
 
 variable (n p q l : Type _) (R : Type u₂)
 

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

@@ -132,10 +132,7 @@ theorem sl_non_abelian [Fintype n] [Nontrivial R] (h : 1 < Fintype.card n) :
   let A := Eb R i j hij
   let B := Eb R j i hij.symm
   intro c
-  have c' : A.val ⬝ B.val = B.val ⬝ A.val :=
-    by
-    rw [← sub_eq_zero, ← sl_bracket, c.trivial]
-    rfl
+  have c' : A.val ⬝ B.val = B.val ⬝ A.val := by rw [← sub_eq_zero, ← sl_bracket, c.trivial]; rfl
   simpa [std_basis_matrix, Matrix.mul_apply, hij] using congr_fun (congr_fun c' i) i
 #align lie_algebra.special_linear.sl_non_abelian LieAlgebra.SpecialLinear.sl_non_abelian
 

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

@@ -146,7 +146,7 @@ namespace Symplectic
 /-- The symplectic Lie algebra: skew-adjoint matrices with respect to the canonical skew-symmetric
 bilinear form. -/
 def sp [Fintype l] : LieSubalgebra R (Matrix (Sum l l) (Sum l l) R) :=
-  skewAdjointMatricesLieSubalgebra (Matrix.j l R)
+  skewAdjointMatricesLieSubalgebra (Matrix.J l R)
 #align lie_algebra.symplectic.sp LieAlgebra.Symplectic.sp
 
 end Symplectic

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -115,7 +115,7 @@ basis of sl n R. -/
 def eb (h : j ≠ i) : sl n R :=
   ⟨Matrix.stdBasisMatrix i j (1 : R),
     show Matrix.stdBasisMatrix i j (1 : R) ∈ LinearMap.ker (Matrix.traceLinearMap n R R) from
-      Matrix.stdBasisMatrix.trace_zero i j (1 : R) h⟩
+      Matrix.StdBasisMatrix.trace_zero i j (1 : R) h⟩
 #align lie_algebra.special_linear.Eb LieAlgebra.SpecialLinear.eb
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module algebra.lie.classical
-! leanprover-community/mathlib commit a5b382d82275e20e2915ef73f679a47224e93409
+! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -378,7 +378,7 @@ theorem indefiniteDiagonal_assoc :
   by
   ext (i j)
   rcases i with ⟨⟨i₁ | i₂⟩ | i₃⟩ <;> rcases j with ⟨⟨j₁ | j₂⟩ | j₃⟩ <;>
-      simp only [indefinite_diagonal, Matrix.diagonal, Equiv.sumAssoc_apply_inl_inl,
+      simp only [indefinite_diagonal, Matrix.diagonal_apply, Equiv.sumAssoc_apply_inl_inl,
         Matrix.reindexLieEquiv_apply, Matrix.submatrix_apply, Equiv.symm_symm, Matrix.reindex_apply,
         Sum.elim_inl, if_true, eq_self_iff_true, Matrix.one_apply_eq, Matrix.fromBlocks_apply₁₁,
         DMatrix.zero_apply, Equiv.sumAssoc_apply_inl_inr, if_false, Matrix.fromBlocks_apply₁₂,

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

@@ -89,7 +89,7 @@ theorem matrix_trace_commutator_zero [Fintype n] (X Y : Matrix n n R) : Matrix.t
   calc
     _ = Matrix.trace (X ⬝ Y) - Matrix.trace (Y ⬝ X) := trace_sub _ _
     _ = Matrix.trace (X ⬝ Y) - Matrix.trace (X ⬝ Y) :=
-      congr_arg (fun x => _ - x) (Matrix.trace_mul_comm Y X)
+      (congr_arg (fun x => _ - x) (Matrix.trace_mul_comm Y X))
     _ = 0 := sub_self _
     
 #align lie_algebra.matrix_trace_commutator_zero LieAlgebra.matrix_trace_commutator_zero

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -76,9 +76,7 @@ open Matrix
 open scoped Matrix
 
 variable (n p q l : Type*) (R : Type u₂)
-
 variable [DecidableEq n] [DecidableEq p] [DecidableEq q] [DecidableEq l]
-
 variable [CommRing R]
 
 @[simp]

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -272,7 +272,6 @@ theorem jd_transform [Fintype l] : (PD l R)ᵀ * JD l R * PD l R = (2 : R) • S
   have h : (PD l R)ᵀ * JD l R = Matrix.fromBlocks 1 1 1 (-1) := by
     simp [PD, JD, Matrix.fromBlocks_transpose, Matrix.fromBlocks_multiply]
   rw [h, PD, s_as_blocks, Matrix.fromBlocks_multiply, Matrix.fromBlocks_smul]
-  congr
   simp [two_smul]
 #align lie_algebra.orthogonal.JD_transform LieAlgebra.Orthogonal.jd_transform
 

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

@@ -129,7 +129,7 @@ theorem sl_non_abelian [Fintype n] [Nontrivial R] (h : 1 < Fintype.card n) :
   intro c
   have c' : A.val * B.val = B.val * A.val := by
     rw [← sub_eq_zero, ← sl_bracket, c.trivial, ZeroMemClass.coe_zero]
-  simpa [stdBasisMatrix, Matrix.mul_apply, hij] using congr_fun (congr_fun c' i) i
+  simpa [A, B, stdBasisMatrix, Matrix.mul_apply, hij] using congr_fun (congr_fun c' i) i
 #align lie_algebra.special_linear.sl_non_abelian LieAlgebra.SpecialLinear.sl_non_abelian
 
 end SpecialLinear

This reverts commit f3695eb2.

@@ -224,8 +224,9 @@ def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Su
 theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (Sum p q) (Sum p q) R) =
       (Pso p q R i)⁻¹ * (A : Matrix (Sum p q) (Sum p q) R) * Pso p q R i := by
-  rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply,
-    skewAdjointMatricesLieSubalgebraEquiv_apply]
+  rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [skewAdjointMatricesLieSubalgebraEquiv_apply]
 #align lie_algebra.orthogonal.so_indefinite_equiv_apply LieAlgebra.Orthogonal.soIndefiniteEquiv_apply
 
 /-- A matrix defining a canonical even-rank symmetric bilinear form.

This reverts commit 26eb2b0a.

@@ -224,9 +224,8 @@ def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Su
 theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (Sum p q) (Sum p q) R) =
       (Pso p q R i)⁻¹ * (A : Matrix (Sum p q) (Sum p q) R) * Pso p q R i := by
-  rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply]
-  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
-  erw [skewAdjointMatricesLieSubalgebraEquiv_apply]
+  rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply,
+    skewAdjointMatricesLieSubalgebraEquiv_apply]
 #align lie_algebra.orthogonal.so_indefinite_equiv_apply LieAlgebra.Orthogonal.soIndefiniteEquiv_apply
 
 /-- A matrix defining a canonical even-rank symmetric bilinear form.

This includes all the changes from #7606.

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

@@ -224,8 +224,9 @@ def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Su
 theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (Sum p q) (Sum p q) R) =
       (Pso p q R i)⁻¹ * (A : Matrix (Sum p q) (Sum p q) R) * Pso p q R i := by
-  rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply,
-    skewAdjointMatricesLieSubalgebraEquiv_apply]
+  rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply]
+  -- This used to be `rw`, but we need `erw` after leanprover/lean4#2644
+  erw [skewAdjointMatricesLieSubalgebraEquiv_apply]
 #align lie_algebra.orthogonal.so_indefinite_equiv_apply LieAlgebra.Orthogonal.soIndefiniteEquiv_apply
 
 /-- A matrix defining a canonical even-rank symmetric bilinear form.

Mathlib.Algebra.Invertible is used by fundamental tactics, and this essentially splits it into the part used by NormNum, and everything else.

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

@@ -3,7 +3,6 @@ Copyright (c) 2020 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathlib.Algebra.Invertible
 import Mathlib.Data.Matrix.Basis
 import Mathlib.Data.Matrix.DMatrix
 import Mathlib.Algebra.Lie.Abelian

@@ -291,7 +291,7 @@ def typeDEquivSo' [Fintype l] [Invertible (2 : R)] : typeD l R ≃ₗ⁅R⁆ so'
   apply (skewAdjointMatricesLieSubalgebraEquiv (JD l R) (PD l R) (by infer_instance)).trans
   apply LieEquiv.ofEq
   ext A
-  rw [jd_transform, ← unitOfInvertible_val (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
+  rw [jd_transform, ← val_unitOfInvertible (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
     mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   rfl
 #align lie_algebra.orthogonal.type_D_equiv_so' LieAlgebra.Orthogonal.typeDEquivSo'
@@ -380,7 +380,7 @@ def typeBEquivSo' [Invertible (2 : R)] : typeB l R ≃ₗ⁅R⁆ so' (Sum Unit l
         (Matrix.reindexAlgEquiv _ (Equiv.sumAssoc PUnit l l)) (Matrix.transpose_reindex _ _)).trans
   apply LieEquiv.ofEq
   ext A
-  rw [jb_transform, ← unitOfInvertible_val (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
+  rw [jb_transform, ← val_unitOfInvertible (2 : R), ← Units.smul_def, LieSubalgebra.mem_coe,
     LieSubalgebra.mem_coe, mem_skewAdjointMatricesLieSubalgebra_unit_smul]
   simp [indefiniteDiagonal_assoc, S]
 #align lie_algebra.orthogonal.type_B_equiv_so' LieAlgebra.Orthogonal.typeBEquivSo'

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).

@@ -85,8 +85,8 @@ variable [CommRing R]
 @[simp]
 theorem matrix_trace_commutator_zero [Fintype n] (X Y : Matrix n n R) : Matrix.trace ⁅X, Y⁆ = 0 :=
   calc
-    _ = Matrix.trace (X ⬝ Y) - Matrix.trace (Y ⬝ X) := trace_sub _ _
-    _ = Matrix.trace (X ⬝ Y) - Matrix.trace (X ⬝ Y) :=
+    _ = Matrix.trace (X * Y) - Matrix.trace (Y * X) := trace_sub _ _
+    _ = Matrix.trace (X * Y) - Matrix.trace (X * Y) :=
       (congr_arg (fun x => _ - x) (Matrix.trace_mul_comm Y X))
     _ = 0 := sub_self _
 #align lie_algebra.matrix_trace_commutator_zero LieAlgebra.matrix_trace_commutator_zero
@@ -99,7 +99,7 @@ def sl [Fintype n] : LieSubalgebra R (Matrix n n R) :=
     lie_mem' := fun _ _ => LinearMap.mem_ker.2 <| matrix_trace_commutator_zero _ _ _ _ }
 #align lie_algebra.special_linear.sl LieAlgebra.SpecialLinear.sl
 
-theorem sl_bracket [Fintype n] (A B : sl n R) : ⁅A, B⁆.val = A.val ⬝ B.val - B.val ⬝ A.val :=
+theorem sl_bracket [Fintype n] (A B : sl n R) : ⁅A, B⁆.val = A.val * B.val - B.val * A.val :=
   rfl
 #align lie_algebra.special_linear.sl_bracket LieAlgebra.SpecialLinear.sl_bracket
 
@@ -128,7 +128,7 @@ theorem sl_non_abelian [Fintype n] [Nontrivial R] (h : 1 < Fintype.card n) :
   let A := Eb R i j hij
   let B := Eb R j i hij.symm
   intro c
-  have c' : A.val ⬝ B.val = B.val ⬝ A.val := by
+  have c' : A.val * B.val = B.val * A.val := by
     rw [← sub_eq_zero, ← sl_bracket, c.trivial, ZeroMemClass.coe_zero]
   simpa [stdBasisMatrix, Matrix.mul_apply, hij] using congr_fun (congr_fun c' i) i
 #align lie_algebra.special_linear.sl_non_abelian LieAlgebra.SpecialLinear.sl_non_abelian
@@ -198,7 +198,7 @@ def invertiblePso {i : R} (hi : i * i = -1) : Invertible (Pso p q R i) :=
 #align lie_algebra.orthogonal.invertible_Pso LieAlgebra.Orthogonal.invertiblePso
 
 theorem indefiniteDiagonal_transform {i : R} (hi : i * i = -1) :
-    (Pso p q R i)ᵀ ⬝ indefiniteDiagonal p q R ⬝ Pso p q R i = 1 := by
+    (Pso p q R i)ᵀ * indefiniteDiagonal p q R * Pso p q R i = 1 := by
   ext (x y); rcases x with ⟨x⟩|⟨x⟩ <;> rcases y with ⟨y⟩|⟨y⟩
   · -- x y : p
     by_cases h : x = y <;>
@@ -224,7 +224,7 @@ def soIndefiniteEquiv {i : R} (hi : i * i = -1) : so' p q R ≃ₗ⁅R⁆ so (Su
 
 theorem soIndefiniteEquiv_apply {i : R} (hi : i * i = -1) (A : so' p q R) :
     (soIndefiniteEquiv p q R hi A : Matrix (Sum p q) (Sum p q) R) =
-      (Pso p q R i)⁻¹ ⬝ (A : Matrix (Sum p q) (Sum p q) R) ⬝ Pso p q R i := by
+      (Pso p q R i)⁻¹ * (A : Matrix (Sum p q) (Sum p q) R) * Pso p q R i := by
   rw [soIndefiniteEquiv, LieEquiv.trans_apply, LieEquiv.ofEq_apply,
     skewAdjointMatricesLieSubalgebraEquiv_apply]
 #align lie_algebra.orthogonal.so_indefinite_equiv_apply LieAlgebra.Orthogonal.soIndefiniteEquiv_apply
@@ -268,8 +268,8 @@ theorem s_as_blocks : S l R = Matrix.fromBlocks 1 0 0 (-1) := by
   rfl
 #align lie_algebra.orthogonal.S_as_blocks LieAlgebra.Orthogonal.s_as_blocks
 
-theorem jd_transform [Fintype l] : (PD l R)ᵀ ⬝ JD l R ⬝ PD l R = (2 : R) • S l R := by
-  have h : (PD l R)ᵀ ⬝ JD l R = Matrix.fromBlocks 1 1 1 (-1) := by
+theorem jd_transform [Fintype l] : (PD l R)ᵀ * JD l R * PD l R = (2 : R) • S l R := by
+  have h : (PD l R)ᵀ * JD l R = Matrix.fromBlocks 1 1 1 (-1) := by
     simp [PD, JD, Matrix.fromBlocks_transpose, Matrix.fromBlocks_multiply]
   rw [h, PD, s_as_blocks, Matrix.fromBlocks_multiply, Matrix.fromBlocks_smul]
   congr
@@ -277,7 +277,7 @@ theorem jd_transform [Fintype l] : (PD l R)ᵀ ⬝ JD l R ⬝ PD l R = (2 : R) 
 #align lie_algebra.orthogonal.JD_transform LieAlgebra.Orthogonal.jd_transform
 
 theorem pd_inv [Fintype l] [Invertible (2 : R)] : PD l R * ⅟ (2 : R) • (PD l R)ᵀ = 1 := by
-  rw [PD, Matrix.fromBlocks_transpose, Matrix.fromBlocks_smul, Matrix.mul_eq_mul,
+  rw [PD, Matrix.fromBlocks_transpose, Matrix.fromBlocks_smul,
     Matrix.fromBlocks_multiply]
   simp
 #align lie_algebra.orthogonal.PD_inv LieAlgebra.Orthogonal.pd_inv
@@ -342,7 +342,7 @@ def PB :=
 variable [Fintype l]
 
 theorem pb_inv [Invertible (2 : R)] : PB l R * Matrix.fromBlocks 1 0 0 (⅟ (PD l R)) = 1 := by
-  rw [PB, Matrix.mul_eq_mul, Matrix.fromBlocks_multiply, Matrix.mul_invOf_self]
+  rw [PB, Matrix.fromBlocks_multiply, mul_invOf_self]
   simp only [Matrix.mul_zero, Matrix.mul_one, Matrix.zero_mul, zero_add, add_zero,
     Matrix.fromBlocks_one]
 #align lie_algebra.orthogonal.PB_inv LieAlgebra.Orthogonal.pb_inv
@@ -351,7 +351,7 @@ instance invertiblePB [Invertible (2 : R)] : Invertible (PB l R) :=
   invertibleOfRightInverse _ _ (pb_inv l R)
 #align lie_algebra.orthogonal.invertible_PB LieAlgebra.Orthogonal.invertiblePB
 
-theorem jb_transform : (PB l R)ᵀ ⬝ JB l R ⬝ PB l R = (2 : R) • Matrix.fromBlocks 1 0 0 (S l R) := by
+theorem jb_transform : (PB l R)ᵀ * JB l R * PB l R = (2 : R) • Matrix.fromBlocks 1 0 0 (S l R) := by
   simp [PB, JB, jd_transform, Matrix.fromBlocks_transpose, Matrix.fromBlocks_multiply,
     Matrix.fromBlocks_smul]
 #align lie_algebra.orthogonal.JB_transform LieAlgebra.Orthogonal.jb_transform

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

This has nice performance benefits.

@@ -76,7 +76,7 @@ open Matrix
 
 open scoped Matrix
 
-variable (n p q l : Type _) (R : Type u₂)
+variable (n p q l : Type*) (R : Type u₂)
 
 variable [DecidableEq n] [DecidableEq p] [DecidableEq q] [DecidableEq l]
 

@@ -47,7 +47,7 @@ which approach should be preferred so the choice should be assumed to be somewha
 ### Diagonal quadratic form or diagonal Cartan subalgebra
 
 For the algebras of type `B` and `D`, there are two natural definitions. For example since the
-the `2l × 2l` matrix:
+`2l × 2l` matrix:
 $$
   J = \left[\begin{array}{cc}
               0_l & 1_l\\

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module algebra.lie.classical
-! leanprover-community/mathlib commit 3e068ece210655b7b9a9477c3aff38a492400aa1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Invertible
 import Mathlib.Data.Matrix.Basis
@@ -16,6 +11,8 @@ import Mathlib.LinearAlgebra.Matrix.Trace
 import Mathlib.Algebra.Lie.SkewAdjoint
 import Mathlib.LinearAlgebra.SymplecticGroup
 
+#align_import algebra.lie.classical from "leanprover-community/mathlib"@"3e068ece210655b7b9a9477c3aff38a492400aa1"
+
 /-!
 # Classical Lie algebras
 

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

@@ -363,9 +363,8 @@ theorem indefiniteDiagonal_assoc :
     indefiniteDiagonal (Sum Unit l) l R =
       Matrix.reindexLieEquiv (Equiv.sumAssoc Unit l l).symm
         (Matrix.fromBlocks 1 0 0 (indefiniteDiagonal l l R)) := by
-  ext (i j)
+  ext ⟨⟨i₁ | i₂⟩ | i₃⟩ ⟨⟨j₁ | j₂⟩ | j₃⟩ <;>
   -- Porting note: added `Sum.inl_injective.eq_iff`, `Sum.inr_injective.eq_iff`
-  rcases i with ⟨⟨i₁ | i₂⟩ | i₃⟩ <;> rcases j with ⟨⟨j₁ | j₂⟩ | j₃⟩ <;>
     simp only [indefiniteDiagonal, Matrix.diagonal_apply, Equiv.sumAssoc_apply_inl_inl,
       Matrix.reindexLieEquiv_apply, Matrix.submatrix_apply, Equiv.symm_symm, Matrix.reindex_apply,
       Sum.elim_inl, if_true, eq_self_iff_true, Matrix.one_apply_eq, Matrix.fromBlocks_apply₁₁,