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refactor: Replace simp proofs

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jstoobysmith 2024-08-30 13:40:32 -04:00
parent cd04e13ced
commit 064a5ebbfe
23 changed files with 110 additions and 148 deletions
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17
HepLean/SpaceTime/MinkowskiMetric.lean
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@ -45,8 +45,8 @@ lemma sq : @minkowskiMatrix d * minkowskiMatrix = 1 := by
subst h
simp_all only [one_apply_eq]
· simp_all only [ne_eq, Sum.inl.injEq, not_false_eq_true, one_apply_ne]
· simp only [ne_eq, not_false_eq_true, diagonal_apply_ne, one_apply_ne]
· simp only [ne_eq, not_false_eq_true, diagonal_apply_ne, one_apply_ne]
· rfl
· rfl
· simp only [diagonal, of_apply, Sum.inr.injEq, Sum.elim_inr, mul_neg, mul_one, neg_neg]
split
· rename_i h
@ -191,7 +191,7 @@ lemma self_spaceReflection_eq_zero_iff : ⟪v, v.spaceReflection⟫ₘ = 0 ↔ v
exact h3
· simpa using congrFun h4 i
· rw [h]
simp only [map_zero, LinearMap.zero_apply]
exact LinearMap.map_zero₂ minkowskiMetric (spaceReflection 0)
/-!
# Non degeneracy of the Minkowski metric
@ -339,16 +339,7 @@ lemma on_basis (μ ν : Fin 1 ⊕ Fin d) : ⟪e μ, e ν⟫ₘ = η μ ν := by
lemma matrix_apply_stdBasis (ν μ : Fin 1 ⊕ Fin d) :
Λ ν μ = η ν ν * ⟪e ν, Λ *ᵥ e μ⟫ₘ := by
rw [on_basis_mulVec, ← mul_assoc]
have h1 : η ν ν * η ν ν = 1 := by
simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
rcases μ
· rcases ν
· simp_all only [Sum.elim_inl, mul_one]
· simp_all only [Sum.elim_inr, mul_neg, mul_one, neg_neg]
· rcases ν
· simp_all only [Sum.elim_inl, mul_one]
· simp_all only [Sum.elim_inr, mul_neg, mul_one, neg_neg]
simp [h1]
simp [η_apply_mul_η_apply_diag ν]
end matrices
end minkowskiMetric