refactor: Remove double empty lines

This commit is contained in:
jstoobysmith 2024-07-03 07:56:30 -04:00
parent ae18a2196d
commit f03d063c86
60 changed files with 0 additions and 232 deletions

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@ -17,7 +17,6 @@ We define
-/
namespace SpaceTime
open Matrix
open TensorProduct
@ -34,7 +33,6 @@ lemma transpose_eta (A : lorentzAlgebra) : A.1ᵀ * η = - η * A.1 := by
erw [mem_skewAdjointMatricesLieSubalgebra] at h1
simpa [LieAlgebra.Orthogonal.so', IsSkewAdjoint, IsAdjointPair] using h1
lemma mem_of_transpose_eta_eq_eta_mul_self {A : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) }
(h : Aᵀ * η = - η * A) : A ∈ lorentzAlgebra := by
erw [mem_skewAdjointMatricesLieSubalgebra]
@ -58,7 +56,6 @@ lemma mem_iff' (A : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ) :
rw [minkowskiMatrix.sq]
all_goals noncomm_ring
lemma diag_comp (Λ : lorentzAlgebra) (μ : Fin 1 ⊕ Fin 3) : Λ.1 μ μ = 0 := by
have h := congrArg (fun M ↦ M μ μ) $ mem_iff.mp Λ.2
simp only [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, mul_diagonal,
@ -67,22 +64,18 @@ lemma diag_comp (Λ : lorentzAlgebra) (μ : Fin 1 ⊕ Fin 3) : Λ.1 μ μ = 0 :=
simpa using h
simpa using h
lemma time_comps (Λ : lorentzAlgebra) (i : Fin 3) :
Λ.1 (Sum.inr i) (Sum.inl 0) = Λ.1 (Sum.inl 0) (Sum.inr i) := by
simpa only [Fin.isValue, minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, mul_diagonal,
transpose_apply, Sum.elim_inr, mul_neg, mul_one, diagonal_neg, diagonal_mul, Sum.elim_inl,
neg_mul, one_mul, neg_inj] using congrArg (fun M ↦ M (Sum.inl 0) (Sum.inr i)) $ mem_iff.mp Λ.2
lemma space_comps (Λ : lorentzAlgebra) (i j : Fin 3) :
Λ.1 (Sum.inr i) (Sum.inr j) = - Λ.1 (Sum.inr j) (Sum.inr i) := by
simpa only [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, diagonal_neg, diagonal_mul,
Sum.elim_inr, neg_neg, one_mul, mul_diagonal, transpose_apply, mul_neg, mul_one] using
(congrArg (fun M ↦ M (Sum.inr i) (Sum.inr j)) $ mem_iff.mp Λ.2).symm
end lorentzAlgebra
@[simps!]
@ -104,5 +97,4 @@ instance spaceTimeAsLieModule : LieModule lorentzAlgebra (LorentzVector 3) w
simp [Bracket.bracket]
rw [mulVec_smul]
end SpaceTime