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refactor: Replace FDiscrete with FD

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jstoobysmith 2024-11-05 14:37:10 +00:00
parent bfaaf36485
commit 5acf22c479
9 changed files with 223 additions and 223 deletions
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18
HepLean/Tensors/Tree/NodeIdentities/PermContr.lean
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@ -32,13 +32,13 @@ 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.pairτ S.FD 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.pairτ S.FD 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]
@ -51,7 +51,7 @@ lemma contrFin1Fin1_naturality {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
Functor.comp_obj, Discrete.functor_obj_eq_as, Function.comp_apply, CategoryStruct.comp,
extractOne_homToEquiv, Action.Hom.comp_hom, LinearMap.coe_comp]
trans (S.F.map (extractTwoAux' i j σ)).hom (PiTensorProduct.tprod S.k (fun k =>
match k with | Sum.inl 0 => x | Sum.inr 0 => (S.FDiscrete.map
match k with | Sum.inl 0 => x | Sum.inr 0 => (S.FD.map
(eqToHom (by
simp only [Nat.succ_eq_add_one, Discrete.functor_obj_eq_as, Function.comp_apply,
extractOne_homToEquiv, Fin.isValue, mk_hom, finExtractTwo_symm_inl_inr_apply,
@ -72,10 +72,10 @@ lemma contrFin1Fin1_naturality {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
| Sum.inl 0 => rfl
| Sum.inr 0 => rfl
change _ = (S.contrFin1Fin1 c1 i j h).inv.hom
((S.FDiscrete.map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i))).hom x ⊗ₜ[S.k]
(S.FDiscrete.map (Discrete.eqToHom (congrArg S.τ (Hom.toEquiv_comp_inv_apply σ i)))).hom y)
((S.FD.map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i))).hom x ⊗ₜ[S.k]
(S.FD.map (Discrete.eqToHom (congrArg S.τ (Hom.toEquiv_comp_inv_apply σ i)))).hom y)
rw [contrFin1Fin1_inv_tmul]
change ((lift.obj S.FDiscrete).map (extractTwoAux' i j σ)).hom _ = _
change ((lift.obj S.FD).map (extractTwoAux' i j σ)).hom _ = _
rw [lift.map_tprod]
apply congrArg
funext i
@ -86,8 +86,8 @@ 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.FD.map (eqToHom _)) ≫ S.FD.map (eqToHom _)).hom y =
((S.FD.map (eqToHom _)) ≫ S.FD.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]
@ -154,7 +154,7 @@ lemma contrIso_comm_aux_3 {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
/-- A helper function used to proof the relation between perm and contr. -/
def contrIsoComm {n : ℕ} {c c1 : Fin n.succ.succ → S.C}
{i : Fin n.succ.succ} {j : Fin n.succ} (σ : (OverColor.mk c) ⟶ (OverColor.mk c1)) :=
(((Discrete.pairτ S.FDiscrete S.τ).map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i) :
(((Discrete.pairτ S.FD S.τ).map (Discrete.eqToHom (Hom.toEquiv_comp_inv_apply σ i) :
(Discrete.mk (c ((Hom.toEquiv σ).symm i))) ⟶
(Discrete.mk (c1 i)))) ⊗ (S.F.map (extractTwo i j σ)))