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chore: bump toolchain to v4.15.0

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#281 adapt code to v4.15.0 and fix long heartbeats, e.g., toDualRep_apply_eq_contrOneTwoLeft.

---------

Co-authored-by: jstoobysmith <72603918+jstoobysmith@users.noreply.github.com>
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KUO-TSAN HSU (Gordon) 2025-01-20 15:42:53 +08:00 • committed by GitHub
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28
HepLean/Tensors/Tree/NodeIdentities/Basic.lean
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@ -301,7 +301,7 @@ lemma contr_action {n : ℕ} {c : Fin n.succ.succ → S.C} {i : Fin n.succ.succ}
{h : c (i.succAbove j) = S.τ (c i)} (g : S.G) (t : TensorTree S c) :
(contr i j h (action g t)).tensor = (action g (contr i j h t)).tensor := by
simp only [Nat.succ_eq_add_one, contr_tensor, action_tensor]
change ((S.F.obj (OverColor.mk c)).ρ g ≫ (S.contrMap c i j h).hom) t.tensor = _
change (ModuleCat.ofHom ((S.F.obj (OverColor.mk c)).ρ g) ≫ (S.contrMap c i j h).hom) t.tensor = _
erw [(S.contrMap c i j h).comm g]
rfl
@ -311,16 +311,16 @@ lemma prod_action {n n1 : ℕ} {c : Fin n → S.C} {c1 : Fin n1 → S.C} (g : S.
(prod (action g t) (action g t1)).tensor = (action g (prod t t1)).tensor := by
simp only [prod_tensor, action_tensor, map_tmul]
change _ = ((S.F.map (equivToIso finSumFinEquiv).hom).hom ≫
(S.F.obj (OverColor.mk (Sum.elim c c1 ∘ ⇑finSumFinEquiv.symm))).ρ g)
ModuleCat.ofHom ((S.F.obj (OverColor.mk (Sum.elim c c1 ∘ ⇑finSumFinEquiv.symm))).ρ g))
(((Functor.LaxMonoidal.μ S.F (OverColor.mk c) (OverColor.mk c1)).hom
(t.tensor ⊗ₜ[S.k] t1.tensor)))
erw [← (S.F.map (equivToIso finSumFinEquiv).hom).comm g]
simp only [Action.forget_obj, Functor.id_obj, mk_hom, Action.instMonoidalCategory_tensorObj_V,
Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
Action.FunctorCategoryEquivalence.functor_obj_obj, ModuleCat.coe_comp, Function.comp_apply]
Action.FunctorCategoryEquivalence.functor_obj_obj, ModuleCat.hom_comp, Function.comp_apply]
change _ = (S.F.map (equivToIso finSumFinEquiv).hom).hom
(((Functor.LaxMonoidal.μ S.F (OverColor.mk c) (OverColor.mk c1)).hom ≫
(S.F.obj (OverColor.mk (Sum.elim c c1))).ρ g) (t.tensor ⊗ₜ[S.k] t1.tensor))
ModuleCat.ofHom ((S.F.obj (OverColor.mk (Sum.elim c c1))).ρ g)) (t.tensor ⊗ₜ[S.k] t1.tensor))
erw [← (Functor.LaxMonoidal.μ S.F (OverColor.mk c) (OverColor.mk c1)).comm g]
rfl
@ -334,7 +334,7 @@ lemma perm_action {n m : ℕ} {c : Fin n → S.C} {c1 : Fin m → S.C}
(σ : (OverColor.mk c) ⟶ (OverColor.mk c1)) (g : S.G) (t : TensorTree S c) :
(perm σ (action g t)).tensor = (action g (perm σ t)).tensor := by
simp only [perm_tensor, action_tensor]
change (((S.F.obj (OverColor.mk c)).ρ g) ≫ (S.F.map σ).hom) t.tensor = _
change (ModuleCat.ofHom ((S.F.obj (OverColor.mk c)).ρ g) ≫ (S.F.map σ).hom) t.tensor = _
erw [(S.F.map σ).comm g]
rfl
@ -359,13 +359,14 @@ lemma action_constTwoNode {c1 c2 : S.C}
(g : S.G) : (action g (constTwoNode v)).tensor = (constTwoNode v).tensor := by
simp only [Nat.succ_eq_add_one, Nat.reduceAdd, action_tensor, constTwoNode_tensor,
Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V]
change ((Discrete.pairIsoSep S.FD).hom.hom ≫ (S.F.obj (OverColor.mk ![c1, c2])).ρ g)
((v.hom _)) = _
change ((Discrete.pairIsoSep S.FD).hom.hom ≫
ModuleCat.ofHom ((S.F.obj (OverColor.mk ![c1, c2])).ρ g)) (v.hom _) = _
erw [← (Discrete.pairIsoSep S.FD).hom.comm g]
change ((v.hom ≫ (S.FD.obj { as := c1 } ⊗ S.FD.obj { as := c2 }).ρ g) ≫
(Discrete.pairIsoSep S.FD).hom.hom) _ =_
change ((v.hom ≫ ModuleCat.ofHom ((S.FD.obj { as := c1 } ⊗ S.FD.obj { as := c2 }).ρ g)) ≫
(Discrete.pairIsoSep S.FD).hom.hom) _ = _
erw [← v.comm g]
simp
rfl
/-- An `action` node on a `constThreeNode` leaves the tensor invariant. -/
lemma action_constThreeNode {c1 c2 c3 : S.C}
@ -374,12 +375,13 @@ lemma action_constThreeNode {c1 c2 c3 : S.C}
(g : S.G) : (action g (constThreeNode v)).tensor = (constThreeNode v).tensor := by
simp only [Nat.succ_eq_add_one, Nat.reduceAdd, action_tensor, constThreeNode_tensor,
Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V]
change ((Discrete.tripleIsoSep S.FD).hom.hom ≫ (S.F.obj (OverColor.mk ![c1, c2, c3])).ρ g)
((v.hom _)) = _
change ((Discrete.tripleIsoSep S.FD).hom.hom ≫
ModuleCat.ofHom ((S.F.obj (OverColor.mk ![c1, c2, c3])).ρ g)) (v.hom _) = _
erw [← (Discrete.tripleIsoSep S.FD).hom.comm g]
change ((v.hom ≫ (S.FD.obj { as := c1 } ⊗ S.FD.obj { as := c2 } ⊗
S.FD.obj { as := c3 }).ρ g) ≫ (Discrete.tripleIsoSep S.FD).hom.hom) _ =_
change ((v.hom ≫ ModuleCat.ofHom ((S.FD.obj { as := c1 } ⊗ S.FD.obj { as := c2 } ⊗
S.FD.obj { as := c3 }).ρ g)) ≫ (Discrete.tripleIsoSep S.FD).hom.hom) _ = _
erw [← v.comm g]
simp
rfl
end TensorTree