DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: multiple goal proves

Browse source
This commit is contained in:
jstoobysmith 2024-08-20 14:38:29 -04:00
parent fe0e3c3684
commit c89a7fd1ea
12 changed files with 277 additions and 320 deletions
Download patch file Download diff file Expand all files Collapse all files

10
HepLean/SpaceTime/SL2C/Basic.lean
View file

@ -91,13 +91,9 @@ lemma iff_det_selfAdjoint (Λ : Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ)
toLin LorentzVector.stdBasis LorentzVector.stdBasis Λ ∘ toSelfAdjointMatrix.symm) x).1
= det x.1 := by
rw [LorentzGroup.mem_iff_norm]
apply Iff.intro
intro h x
have h1 := congrArg ofReal $ h (toSelfAdjointMatrix.symm x)
simpa [← det_eq_ηLin] using h1
intro h x
have h1 := h (toSelfAdjointMatrix x)
simpa [det_eq_ηLin] using h1
refine Iff.intro (fun h x => ?_) (fun h x => ?_)
· simpa [← det_eq_ηLin] using congrArg ofReal $ h (toSelfAdjointMatrix.symm x)
· simpa [det_eq_ηLin] using h (toSelfAdjointMatrix x)
/-- Given an element `M ∈ SL(2, ℂ)` the corresponding element of the Lorentz group. -/
@[simps!]