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

23
HepLean/SpaceTime/LorentzTensor/RisingLowering.lean
View file

@ -151,20 +151,19 @@ local infixl:101 " • " => 𝓣.rep
-/
/-! TODO: Move -/
lemma unit_lhs_eq (x : 𝓣.ColorModule μ) (y : 𝓣.ColorModule (𝓣.τ μ) ⊗[R] 𝓣.ColorModule μ) :
contrLeftAux (𝓣.contrDual μ) (x ⊗ₜ[R] y) =
(contrRightAux (𝓣.contrDual (𝓣.τ μ))) ((TensorProduct.comm R _ _) y
⊗ₜ[R] (𝓣.colorModuleCast (𝓣.τ_involutive μ).symm) x) := by
refine TensorProduct.induction_on y (by simp) ?_ (fun z1 z2 h1 h2 => ?_)
intro x1 x2
simp only [contrRightAux, LinearEquiv.refl_toLinearMap, comm_tmul, colorModuleCast,
Equiv.cast_symm, LinearEquiv.coe_mk, Equiv.cast_apply, LinearMap.coe_comp, LinearEquiv.coe_coe,
Function.comp_apply, assoc_tmul, map_tmul, LinearMap.id_coe, id_eq, contrDual_symm', cast_cast,
cast_eq, rid_tmul]
rfl
simp [LinearMap.map_add, add_tmul]
rw [← h1, ← h2, tmul_add, LinearMap.map_add]
· intro x1 x2
simp only [contrRightAux, LinearEquiv.refl_toLinearMap, comm_tmul, colorModuleCast,
Equiv.cast_symm, LinearEquiv.coe_mk, Equiv.cast_apply, LinearMap.coe_comp, LinearEquiv.coe_coe,
Function.comp_apply, assoc_tmul, map_tmul, LinearMap.id_coe, id_eq, contrDual_symm', cast_cast,
cast_eq, rid_tmul]
rfl
· simp only [map_add, add_tmul]
rw [← h1, ← h2, tmul_add, LinearMap.map_add]
@[simp]
lemma unit_lid : (contrRightAux (𝓣.contrDual (𝓣.τ μ))) ((TensorProduct.comm R _ _) (𝓣.unit μ)
@ -250,9 +249,9 @@ lemma dualizeModule_equivariant_apply (g : G) (x : 𝓣.ColorModule μ) :
(𝓣.dualizeModule μ) ((MulActionTensor.repColorModule μ) g x) =
(MulActionTensor.repColorModule (𝓣.τ μ) g) (𝓣.dualizeModule μ x) := by
trans ((𝓣.dualizeModule μ) ∘ₗ ((MulActionTensor.repColorModule μ) g)) x
rfl
rw [dualizeModule_equivariant]
rfl
· rfl
· rw [dualizeModule_equivariant]
rfl
/-- Dualizes the color of all indicies of a tensor by contraction with the metric. -/
def dualizeAll : 𝓣.Tensor cX ≃ₗ[R] 𝓣.Tensor (𝓣.τ ∘ cX) := by