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refactor: Golfing

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This commit is contained in:
jstoobysmith 2024-06-13 08:10:08 -04:00
parent fbda420da9
commit d7b6cf7246
13 changed files with 73 additions and 117 deletions
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4
HepLean/SpaceTime/LorentzAlgebra/Basic.lean
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@ -59,9 +59,7 @@ lemma mem_of_transpose_eta_eq_eta_mul_self {A : Matrix (Fin 4) (Fin 4) ℝ}
simpa [Nat.reduceAdd, reindexLieEquiv_symm, reindexLieEquiv_apply,
LieAlgebra.Orthogonal.so', mem_skewAdjointMatricesLieSubalgebra,
mem_skewAdjointMatricesSubmodule, IsSkewAdjoint, IsAdjointPair, mul_neg] using h1
· change (reindexLieEquiv finSumFinEquiv) _ = _
simp only [Nat.reduceAdd, reindexLieEquiv_symm, reindexLieEquiv_apply, reindex_apply,
Equiv.symm_symm, submatrix_submatrix, Equiv.self_comp_symm, submatrix_id_id]
· exact LieEquiv.apply_symm_apply (reindexLieEquiv finSumFinEquiv) _
lemma mem_iff {A : Matrix (Fin 4) (Fin 4) ℝ} : A ∈ lorentzAlgebra ↔ Aᵀ * η = - η * A :=

7
HepLean/SpaceTime/LorentzAlgebra/Basis.lean
View file

@ -139,10 +139,9 @@ instance : Module.Finite ℝ lorentzAlgebra :=
/-- The Lorentz algebra is 6-dimensional. -/
theorem finrank_eq_six : FiniteDimensional.finrank ℝ lorentzAlgebra = 6 := by
have h := Module.mk_finrank_eq_card_basis σBasis
simp_all
simp [FiniteDimensional.finrank]
rw [h]
simp only [Cardinal.toNat_ofNat]
simp only [finrank_eq_rank, Cardinal.mk_fintype, Fintype.card_fin, Nat.cast_ofNat] at h
exact FiniteDimensional.finrank_eq_of_rank_eq h
end lorentzAlgebra