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refactor: Lint

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jstoobysmith 2024-11-15 10:44:42 +00:00
parent 9763e1240b
commit 05b4d134ec
9 changed files with 51 additions and 40 deletions
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15
HepLean/Tensors/TensorSpecies/ContractLemmas.lean
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@ -34,7 +34,7 @@ lemma contr_two_two_inner_tprod (c : S.C) (x : S.F.obj (OverColor.mk ![c, c]))
CoeSort.coe (S.FD.obj { as := (OverColor.mk ![S.τ c, S.τ c]).hom i }))
(hx : x = PiTensorProduct.tprod S.k fx)
(hy : y = PiTensorProduct.tprod S.k fy) :
{x | μ ν ⊗ y| ν ρ}ᵀ.tensor = (S.F.map (OverColor.mkIso (by
{x | μ ν ⊗ y| ν ρ}ᵀ.tensor = (S.F.map (OverColor.mkIso (by
funext x
fin_cases x <;> rfl)).hom).hom ((OverColor.Discrete.pairIsoSep S.FD).hom.hom
(((S.FD.obj (Discrete.mk c)) ◁ (λ_ (S.FD.obj (Discrete.mk (S.τ c)))).hom).hom
@ -45,13 +45,14 @@ lemma contr_two_two_inner_tprod (c : S.C) (x : S.F.obj (OverColor.mk ![c, c]))
((α_ (S.FD.obj (Discrete.mk (c))) (S.FD.obj (Discrete.mk (c)))
(S.FD.obj (Discrete.mk (S.τ c)) ⊗ S.FD.obj (Discrete.mk (S.τ c)))).hom.hom
(((OverColor.Discrete.pairIsoSep S.FD).inv.hom x ⊗ₜ
(OverColor.Discrete.pairIsoSep S.FD).inv.hom y))))))):= by
(OverColor.Discrete.pairIsoSep S.FD).inv.hom y))))))) := by
subst hx
subst hy
rw [Discrete.pairIsoSep_inv_tprod S.FD fx, Discrete.pairIsoSep_inv_tprod S.FD fy]
change _ = (S.F.map (OverColor.mkIso _).hom).hom ((OverColor.Discrete.pairIsoSep S.FD).hom.hom
((fx (0 : Fin 2) ⊗ₜ[S.k] (λ_ (S.FD.obj { as := S.τ c }).V).hom
((S.contr.app { as := c }).hom (fx (1 : Fin 2) ⊗ₜ[S.k] fy (0 : Fin 2)) ⊗ₜ[S.k] fy (1 : Fin 2)))))
((fx (0 : Fin 2) ⊗ₜ[S.k] (λ_ (S.FD.obj { as := S.τ c }).V).hom
((S.contr.app { as := c }).hom (fx (1 : Fin 2)
⊗ₜ[S.k] fy (0 : Fin 2)) ⊗ₜ[S.k] fy (1 : Fin 2)))))
simp only [F_def, Functor.id_obj, mk_hom, Action.instMonoidalCategory_tensorObj_V,
Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
Action.FunctorCategoryEquivalence.functor_obj_obj, Monoidal.tensorUnit_obj,
@ -86,7 +87,7 @@ lemma contr_two_two_inner_tprod (c : S.C) (x : S.F.obj (OverColor.mk ![c, c]))
Functor.id_obj, instMonoidalCategoryStruct_tensorObj_hom, LinearEquiv.ofLinear_apply]
rfl
/- The tensor. -/
· rw (config := { transparency := .instances }) [Discrete.pairIsoSep_tmul,
· rw (config := { transparency := .instances }) [Discrete.pairIsoSep_tmul,
OverColor.lift.map_tprod]
apply congrArg
funext k
@ -97,7 +98,7 @@ lemma contr_two_two_inner_tprod (c : S.C) (x : S.F.obj (OverColor.mk ![c, c]))
/-- Expands the inner contraction of two 2-tensors in terms of basic categorical
constructions and fields of the tensor species. -/
lemma contr_two_two_inner (c : S.C) (x : S.F.obj (OverColor.mk ![c, c]))
(y : S.F.obj (OverColor.mk ![(S.τ c), (S.τ c)])):
(y : S.F.obj (OverColor.mk ![(S.τ c), (S.τ c)])) :
{x | μ ν ⊗ y| ν ρ}ᵀ.tensor = (S.F.map (OverColor.mkIso (by
funext x
fin_cases x <;> rfl)).hom).hom ((OverColor.Discrete.pairIsoSep S.FD).hom.hom
@ -109,7 +110,7 @@ lemma contr_two_two_inner (c : S.C) (x : S.F.obj (OverColor.mk ![c, c]))
((α_ (S.FD.obj (Discrete.mk (c))) (S.FD.obj (Discrete.mk (c)))
(S.FD.obj (Discrete.mk (S.τ c)) ⊗ S.FD.obj (Discrete.mk (S.τ c)))).hom.hom
(((OverColor.Discrete.pairIsoSep S.FD).inv.hom x ⊗ₜ
(OverColor.Discrete.pairIsoSep S.FD).inv.hom y))))))):= by
(OverColor.Discrete.pairIsoSep S.FD).inv.hom y))))))) := by
simp only [Nat.reduceAdd, Fin.isValue, contr_tensor, prod_tensor, Functor.id_obj, mk_hom,
Action.instMonoidalCategory_tensorObj_V, Equivalence.symm_inverse,
Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,