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feat: unit contract vec

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jstoobysmith 2024-11-18 05:13:21 +00:00
parent 5603a67642
commit 5d21f74062
3 changed files with 55 additions and 23 deletions
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8
HepLean/Tensors/Tree/NodeIdentities/ContrSwap.lean
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@ -74,6 +74,14 @@ def contrSwapHom : (OverColor.mk (c ∘ q.swap.i.succAbove ∘ q.swap.j.succAbov
(OverColor.mk (c ∘ q.i.succAbove ∘ q.j.succAbove)) :=
(mkIso (funext fun x => congrArg c (swap_map_eq q x))).hom
@[simp]
lemma contrSwapHom_toEquiv : Hom.toEquiv q.contrSwapHom = Equiv.refl (Fin n) := by
simp [contrSwapHom]
@[simp]
lemma contrSwapHom_hom_left_apply (x : Fin n) : q.contrSwapHom.hom.left x = x := by
simp [contrSwapHom]
lemma contrMap_swap : q.contrMap = q.swap.contrMap ≫ S.F.map q.contrSwapHom := by
ext x
refine PiTensorProduct.induction_on' x (fun r x => ?_) <| fun x y hx hy => by