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refactor: Contraction of real Lorentz

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jstoobysmith 2024-11-08 10:29:38 +00:00
parent 3cb3340ce0
commit c8aff8f20f
4 changed files with 139 additions and 1 deletions
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9
HepLean/SpaceTime/LorentzGroup/Basic.lean
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@ -137,6 +137,15 @@ variable {Λ Λ' : LorentzGroup d}
lemma coe_inv : (Λ⁻¹).1 = Λ.1⁻¹:= (inv_eq_left_inv (mem_iff_dual_mul_self.mp Λ.2)).symm
instance (M : LorentzGroup d) : Invertible M.1 where
invOf := M⁻¹
invOf_mul_self := by
rw [← coe_inv]
exact (mem_iff_dual_mul_self.mp M.2)
mul_invOf_self := by
rw [← coe_inv]
exact (mem_iff_self_mul_dual.mp M.2)
@[simp]
lemma subtype_inv_mul : (Subtype.val Λ)⁻¹ * (Subtype.val Λ) = 1 := by
trans Subtype.val (Λ⁻¹ * Λ)