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refactor: Simps

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jstoobysmith 2024-11-09 18:06:48 +00:00
parent a7142ef99b
commit e963be5ef8
5 changed files with 20 additions and 18 deletions
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12
HepLean/Lorentz/RealVector/Contraction.lean
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@ -268,7 +268,7 @@ lemma self_parity_eq_zero_iff : ⟪y, (Contr d).ρ LorentzGroup.parity y⟫ₘ =
have hn := Fintype.sum_eq_zero_iff_of_nonneg (f := fun i => y.val i * y.val i) (fun i => by
simpa using mul_self_nonneg (y.val i))
rw [h] at hn
simp at hn
simp only [true_iff] at hn
apply ContrMod.ext
funext i
simpa using congrFun hn i
@ -398,7 +398,9 @@ lemma basis_left {v : Contr d} (μ : Fin 1 ⊕ Fin d) :
rw [as_sum]
rcases μ with μ | μ
· fin_cases μ
simp [minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal]
simp only [Fin.zero_eta, Fin.isValue, ContrMod.stdBasis_apply_same, one_mul,
ContrMod.stdBasis_inl_apply_inr, zero_mul, Finset.sum_const_zero, sub_zero, minkowskiMatrix,
LieAlgebra.Orthogonal.indefiniteDiagonal, diagonal_apply_eq, Sum.elim_inl]
rfl
· simp only [Action.instMonoidalCategory_tensorUnit_V, Fin.isValue, ContrMod.stdBasis_apply,
reduceCtorEq, ↓reduceIte, zero_mul, Sum.inr.injEq, ite_mul, one_mul, Finset.sum_ite_eq,
@ -406,9 +408,9 @@ lemma basis_left {v : Contr d} (μ : Fin 1 ⊕ Fin d) :
diagonal_apply_eq, Sum.elim_inr, neg_mul, neg_inj]
rfl
lemma on_basis_mulVec (μ ν : Fin 1 ⊕ Fin d) : ⟪ContrMod.stdBasis μ, Λ *ᵥ ContrMod.stdBasis ν⟫ₘ = η μ μ * Λ μ ν := by
rw [basis_left]
rw [@ContrMod.mulVec_toFin1dℝ]
lemma on_basis_mulVec (μ ν : Fin 1 ⊕ Fin d) :
⟪ContrMod.stdBasis μ, Λ *ᵥ ContrMod.stdBasis ν⟫ₘ = η μ μ * Λ μ ν := by
rw [basis_left, ContrMod.mulVec_toFin1dℝ]
simp [basis_left, mulVec, dotProduct, ContrMod.stdBasis_apply, ContrMod.toFin1dℝ_eq_val]