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feat: Add symm of unit for complex lorentz

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jstoobysmith 2024-10-24 16:04:05 +00:00
parent 942ee12e60
commit 8c584431c4
3 changed files with 66 additions and 0 deletions
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22
HepLean/SpaceTime/LorentzVector/Complex/Unit.lean
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@ -193,6 +193,28 @@ lemma contr_coContrUnit (x : complexContr) :
simp only [Fin.isValue, one_smul]
repeat rw [add_assoc]
/-!
## Symmetry properties of the units
-/
open CategoryTheory
lemma contrCoUnit_symm :
(contrCoUnit.hom (1 : ℂ)) = (complexContr ◁ 𝟙 _).hom ((β_ complexCo complexContr).hom.hom
(coContrUnit.hom (1 : ℂ))) := by
rw [contrCoUnit_apply_one, contrCoUnitVal_expand_tmul]
rw [coContrUnit_apply_one, coContrUnitVal_expand_tmul]
rfl
lemma coContrUnit_symm :
(coContrUnit.hom (1 : ℂ)) = (complexCo ◁ 𝟙 _).hom ((β_ complexContr complexCo).hom.hom
(contrCoUnit.hom (1 : ℂ))) := by
rw [coContrUnit_apply_one, coContrUnitVal_expand_tmul]
rw [contrCoUnit_apply_one, contrCoUnitVal_expand_tmul]
rfl
end Lorentz
end