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fix: Slow builds with tensors

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jstoobysmith 2024-11-03 08:41:55 +00:00
parent c9c9047a0c
commit e24fd5b40b
3 changed files with 56 additions and 51 deletions
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52
HepLean/Tensors/Tree/NodeIdentities/ProdContr.lean
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@ -139,6 +139,34 @@ lemma sum_inr_succAbove_leftContrI_leftContrJ (k : Fin n1) : finSumFinEquiv.symm
erw [succAbove_leftContrJ_leftContrI_natAdd]
simp
/- An auxillary lemma to `contrMap_prod_tprod`. -/
lemma contrMap_prod_tprod_aux
(l : (OverColor.mk (c ∘ q.i.succAbove ∘ q.j.succAbove)).left ⊕ (OverColor.mk c1).left)
(l' : Fin n.succ.succ ⊕ Fin n1)
(h : Sum.elim c c1 l' = Sum.elim (c ∘ q.i.succAbove ∘ q.j.succAbove) c1 l)
(h' : l' = (Sum.map (q.i.succAbove ∘ q.j.succAbove) id l))
(p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
CoeSort.coe (S.FDiscrete.obj { as := (OverColor.mk c).hom i }))
(q' : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
CoeSort.coe (S.FDiscrete.obj { as := (OverColor.mk c1).hom i })) :
(lift.discreteSumEquiv S.FDiscrete l)
(HepLean.PiTensorProduct.elimPureTensor
(fun k => p (q.i.succAbove (q.j.succAbove k))) q' l) =
(S.FDiscrete.map (eqToHom (by simp [h]))).hom
((lift.discreteSumEquiv S.FDiscrete l')
(HepLean.PiTensorProduct.elimPureTensor p q' l')) := by
subst h'
match l with
| Sum.inl l =>
simp only [instMonoidalCategoryStruct_tensorObj_hom, mk_hom,
Sum.elim_inl, Function.comp_apply, Functor.id_obj, Sum.map_inl, eqToHom_refl,
Discrete.functor_map_id, Action.id_hom, ModuleCat.id_apply]
rfl
| Sum.inr l =>
simp only [instMonoidalCategoryStruct_tensorObj_hom, mk_hom, Sum.elim_inr, Functor.id_obj,
Function.comp_apply, Sum.map_inr, Discrete.functor_map_id, Action.id_hom]
rfl
lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
CoeSort.coe (S.FDiscrete.obj { as := (OverColor.mk c).hom i }))
(q' : (i : (𝟭 Type).obj (OverColor.mk c1).left) →
@ -183,7 +211,6 @@ lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
ModuleCat.id_apply]
rfl
congr 1
/- The contraction. -/
· apply congrArg
simp only [Monoidal.tensorUnit_obj, Action.instMonoidalCategory_tensorUnit_V,
Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
@ -234,28 +261,7 @@ lemma contrMap_prod_tprod (p : (i : (𝟭 Type).obj (OverColor.mk c).left) →
Iso.refl_hom, Action.id_hom, Iso.refl_inv, instMonoidalCategoryStruct_tensorObj_hom,
LinearEquiv.ofLinear_apply, Equiv.toFun_as_coe, equivToIso_mkIso_hom, Equiv.refl_symm,
Functor.mapIso_hom, eqToIso.hom, Functor.mapIso_inv, eqToIso.inv]
have h1 (l : (OverColor.mk (c ∘ q.i.succAbove ∘ q.j.succAbove)).left ⊕ (OverColor.mk c1).left)
(l' : Fin n.succ.succ ⊕ Fin n1)
(h : Sum.elim c c1 l' = Sum.elim (c ∘ q.i.succAbove ∘ q.j.succAbove) c1 l)
(h' : l' = (Sum.map (q.i.succAbove ∘ q.j.succAbove) id l)) :
(lift.discreteSumEquiv S.FDiscrete l)
(HepLean.PiTensorProduct.elimPureTensor
(fun k => p (q.i.succAbove (q.j.succAbove k))) q' l) =
(S.FDiscrete.map (eqToHom (by simp [h]))).hom
((lift.discreteSumEquiv S.FDiscrete l')
(HepLean.PiTensorProduct.elimPureTensor p q' l')) := by
subst h'
match l with
| Sum.inl l =>
simp only [instMonoidalCategoryStruct_tensorObj_hom, mk_hom,
Sum.elim_inl, Function.comp_apply, Functor.id_obj, Sum.map_inl, eqToHom_refl,
Discrete.functor_map_id, Action.id_hom, ModuleCat.id_apply]
rfl
| Sum.inr l =>
simp only [instMonoidalCategoryStruct_tensorObj_hom, mk_hom, Sum.elim_inr, Functor.id_obj,
Function.comp_apply, Sum.map_inr, Discrete.functor_map_id, Action.id_hom]
rfl
refine h1 _ _ ?_ ?_
refine contrMap_prod_tprod_aux _ _ _ ?_ ?_ _ _
· simpa using Discrete.eqToIso.proof_1
(Hom.toEquiv_comp_inv_apply (mkIso (leftContr_map_eq q)).hom k)
· obtain ⟨k, hk⟩ := finSumFinEquiv.surjective k