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

refactor: Lint text

Browse source
This commit is contained in:
jstoobysmith 2024-10-19 09:47:23 +00:00
parent 855dc5146d
commit 1f3ba14462
12 changed files with 168 additions and 127 deletions
Download patch file Download diff file Expand all files Collapse all files

36
HepLean/Tensors/Tree/NodeIdentities/PermContr.lean
View file

@ -30,15 +30,14 @@ lemma contrFin1Fin1_naturality {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
= (S.contrFin1Fin1 c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)
(perm_contr_cond S h σ)).hom.hom
≫ ((Discrete.pairτ S.FDiscrete S.τ).map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i)
: (Discrete.mk (c ((Hom.toEquiv σ).symm i))) ⟶ (Discrete.mk (c1 i)))).hom
:= by
≫ ((Discrete.pairτ S.FDiscrete S.τ).map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i) :
(Discrete.mk (c ((Hom.toEquiv σ).symm i))) ⟶ (Discrete.mk (c1 i)))).hom := by
have h1 : (S.F.map (extractTwoAux' i j σ)) ≫ (S.contrFin1Fin1 c1 i j h).hom
= (S.contrFin1Fin1 c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)
(perm_contr_cond S h σ)).hom
≫ ((Discrete.pairτ S.FDiscrete S.τ).map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i)
: (Discrete.mk (c ((Hom.toEquiv σ).symm i))) ⟶ (Discrete.mk (c1 i)))) := by
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)
(perm_contr_cond S h σ)).hom
≫ ((Discrete.pairτ S.FDiscrete S.τ).map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i) :
(Discrete.mk (c ((Hom.toEquiv σ).symm i))) ⟶ (Discrete.mk (c1 i)))) := by
erw [← CategoryTheory.Iso.eq_comp_inv]
rw [CategoryTheory.Category.assoc]
erw [← CategoryTheory.Iso.inv_comp_eq]
@ -85,7 +84,8 @@ lemma contrFin1Fin1_naturality {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
extractOne_homToEquiv, lift.discreteFunctorMapEqIso, Functor.mapIso_hom, eqToIso.hom,
Functor.mapIso_inv, eqToIso.inv, Functor.id_obj, Discrete.functor_obj_eq_as,
LinearEquiv.ofLinear_apply]
change ((S.FDiscrete.map (eqToHom _)) ≫ S.FDiscrete.map (eqToHom _)).hom y = ((S.FDiscrete.map (eqToHom _)) ≫ S.FDiscrete.map (eqToHom _)).hom y
change ((S.FDiscrete.map (eqToHom _)) ≫ S.FDiscrete.map (eqToHom _)).hom y =
((S.FDiscrete.map (eqToHom _)) ≫ S.FDiscrete.map (eqToHom _)).hom y
rw [← Functor.map_comp, ← Functor.map_comp]
simp only [Fin.isValue, Nat.succ_eq_add_one, Discrete.functor_obj_eq_as, Function.comp_apply,
eqToHom_trans]
@ -97,12 +97,14 @@ lemma contrIso_comm_aux_1 {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
((S.F.map σ).hom ≫ (S.F.map (equivToIso (HepLean.Fin.finExtractTwo i j)).hom).hom) ≫
(S.F.map (mkSum (c1 ∘ ⇑(HepLean.Fin.finExtractTwo i j).symm)).hom).hom =
(S.F.map (equivToIso (HepLean.Fin.finExtractTwo ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j))).hom).hom ≫ (S.F.map
(mkSum (c ∘ ⇑(HepLean.Fin.finExtractTwo ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)).symm)).hom).hom
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j))).hom).hom ≫
(S.F.map (mkSum (c ∘ ⇑(HepLean.Fin.finExtractTwo ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm
((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)).symm)).hom).hom
≫ (S.F.map (extractTwoAux' i j σ ⊗ extractTwoAux i j σ)).hom := by
ext X
change ((S.F.map σ) ≫ (S.F.map (equivToIso (HepLean.Fin.finExtractTwo i j)).hom) ≫ (S.F.map (mkSum (c1 ∘ ⇑(HepLean.Fin.finExtractTwo i j).symm)).hom)).hom X = _
change ((S.F.map σ) ≫ (S.F.map (equivToIso (HepLean.Fin.finExtractTwo i j)).hom) ≫
(S.F.map (mkSum (c1 ∘ ⇑(HepLean.Fin.finExtractTwo i j).symm)).hom)).hom X = _
rw [← Functor.map_comp, ← Functor.map_comp]
erw [extractTwo_finExtractTwo]
simp only [Nat.succ_eq_add_one, extractOne_homToEquiv, Functor.map_comp, Action.comp_hom,
@ -140,8 +142,9 @@ lemma contrIso_comm_aux_3 {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
(S.F.map (extractTwo i j σ)).hom := by
change (S.F.map (extractTwoAux i j σ)).hom ≫ _ = _
have h1 : (S.F.map (extractTwoAux i j σ)) ≫ (S.F.map (mkIso (contrIso.proof_1 S c1 i j)).hom) =
(S.F.map (mkIso (contrIso.proof_1 S c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j))).hom) ≫ (S.F.map (extractTwo i j σ)) := by
(S.F.map (mkIso (contrIso.proof_1 S c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j))).hom) ≫
(S.F.map (extractTwo i j σ)) := by
rw [← Functor.map_comp, ← Functor.map_comp]
apply congrArg
rfl
@ -159,8 +162,9 @@ lemma contrIso_comm_aux_5 {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
(S.F.map (extractTwoAux' i j σ) ⊗ S.F.map (extractTwoAux i j σ)).hom ≫
((S.contrFin1Fin1 c1 i j h).hom.hom ⊗ (S.F.map (mkIso (contrIso.proof_1 S c1 i j)).hom).hom)
= ((S.contrFin1Fin1 c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)
(perm_contr_cond S h σ)).hom.hom ⊗ (S.F.map (mkIso (contrIso.proof_1 S c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j)
(perm_contr_cond S h σ)).hom.hom ⊗
(S.F.map (mkIso (contrIso.proof_1 S c ((Hom.toEquiv σ).symm i)
((HepLean.Fin.finExtractOnePerm ((Hom.toEquiv σ).symm i) (Hom.toEquiv σ)).symm j))).hom).hom)
≫ (S.contrIsoComm σ).hom := by
erw [← CategoryTheory.MonoidalCategory.tensor_comp (f₁ := (S.F.map (extractTwoAux' i j σ)).hom)]