proposition: Lemma TransportedAssocRightOnOb (x y z : C) : TransportedAssocRight ((x,y),z) = # TD (# H (id x) #, TransportedTensorComm Duniv H_eso H_ff TC (y, z)) · TransportedTensorComm Duniv H_eso H_ff TC (x, TC (y,z)).
proof: Proof. cbn. rewrite ! id_left. rewrite ! id_right. rewrite ! functor_id. rewrite ! assoc. apply maponpaths_2. fold (TransportedTensor Duniv H_eso H_ff). etrans. { apply (! functor_comp TD _ _). } apply maponpaths. rewrite <- binprod_comp. rewrite id_right. apply maponpaths. etrans. { apply maponpaths_2. apply (functor_id TD). } apply id_left. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit