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refactor: Lint

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jstoobysmith 2024-08-06 15:56:29 -04:00
parent d02e94886d
commit cecec0c843
7 changed files with 52 additions and 43 deletions
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16
HepLean/SpaceTime/LorentzTensor/Basic.lean
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@ -105,11 +105,15 @@ variable {𝓒 : TensorColor} [Fintype 𝓒.Color] [DecidableEq 𝓒.Color]
variable (cX : ColorMap 𝓒 X) (cY : ColorMap 𝓒 Y) (cZ : ColorMap 𝓒 Z)
/-- A relation, given an equivalence of types, between ColorMap which is true
if related by composition of the equivalence. -/
def MapIso (e : X ≃ Y) (cX : ColorMap 𝓒 X) (cY : ColorMap 𝓒 Y) : Prop := cX = cY ∘ e
/-- The sum of two color maps, formed by `Sum.elim`. -/
def sum (cX : ColorMap 𝓒 X) (cY : ColorMap 𝓒 Y) : ColorMap 𝓒 (Sum X Y) :=
Sum.elim cX cY
/-- The dual of a color map, formed by composition with `𝓒.τ`. -/
def dual (cX : ColorMap 𝓒 X) : ColorMap 𝓒 X := 𝓒.τ ∘ cX
namespace MapIso
@ -127,7 +131,7 @@ lemma trans (h : cX.MapIso e cY) (h' : cY.MapIso e' cZ) :
subst h h'
simp
lemma sum {eX : X ≃ X'} {eY : Y ≃ Y'} (hX : cX.MapIso eX cX') (hY : cY.MapIso eY cY') :
lemma sum {eX : X ≃ X'} {eY : Y ≃ Y'} (hX : cX.MapIso eX cX') (hY : cY.MapIso eY cY') :
(cX.sum cY).MapIso (eX.sumCongr eY) (cX'.sum cY') := by
funext x
subst hX hY
@ -136,7 +140,7 @@ lemma sum {eX : X ≃ X'} {eY : Y ≃ Y'} (hX : cX.MapIso eX cX') (hY : cY.MapI
| Sum.inr x => rfl
lemma dual {e : X ≃ Y} (h : cX.MapIso e cY) :
cX.dual.MapIso e cY.dual := by
cX.dual.MapIso e cY.dual := by
subst h
rfl
@ -569,9 +573,10 @@ lemma tensoratorEquiv_tmul_tprod (p : 𝓣.PureTensor cX) (q : 𝓣.PureTensor c
@[simp]
lemma tensoratorEquiv_symm_tprod (f : 𝓣.PureTensor (Sum.elim cX cY)) :
(𝓣.tensoratorEquiv cX cY).symm ((PiTensorProduct.tprod R) f) =
(PiTensorProduct.tprod R) (𝓣.inlPureTensor f) ⊗ₜ[R] (PiTensorProduct.tprod R) (𝓣.inrPureTensor f) := by
(PiTensorProduct.tprod R) (𝓣.inlPureTensor f) ⊗ₜ[R]
(PiTensorProduct.tprod R) (𝓣.inrPureTensor f) := by
simp [tensoratorEquiv, tensorator]
change (PiTensorProduct.lift 𝓣.domCoprod) ((PiTensorProduct.tprod R) f) = _
change (PiTensorProduct.lift 𝓣.domCoprod) ((PiTensorProduct.tprod R) f) = _
simp [domCoprod]
@[simp]
@ -669,11 +674,12 @@ lemma contrDual_symm_contrRightAux_apply_tmul (h : ν = η)
-/
/-- The equivalence between `𝓣.Tensor cX` and `R` when the indexing set `X` is empty. -/
def isEmptyEquiv [IsEmpty X] : 𝓣.Tensor cX ≃ₗ[R] R :=
PiTensorProduct.isEmptyEquiv X
@[simp]
def isEmptyEquiv_tprod [IsEmpty X] (f : 𝓣.PureTensor cX) :
lemma isEmptyEquiv_tprod [IsEmpty X] (f : 𝓣.PureTensor cX) :
𝓣.isEmptyEquiv (PiTensorProduct.tprod R f) = 1 := by
simp only [isEmptyEquiv]
erw [PiTensorProduct.isEmptyEquiv_apply_tprod]