proposition: Lemma cwf_square_comm {Γ} {A} {ΓA : C} {π : ΓA --> Γ} {t : Tm ΓA : hSet} (e : (pp : nat_trans _ _) _ t = functor_on_morphisms Ty π A) : @paths _ (@compose _ _ (@functor_on_objects _ (functor_category _ HSET_univalent_category) _ Γ) Ty (functor_on_morphisms _ π) (pr1weq (@yy C Ty Γ) A)) (@compose _ (@functor_on_objects _ (functor_category _ hset_category) _ ΓA) Tm Ty (pr1weq (@yy C Tm ΓA) t) pp).
proof: Proof. apply pathsinv0. etrans. 2: apply yy_natural. etrans. { apply yy_comp_nat_trans. } apply maponpaths, e. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.DisplayedBicats.Examples.ContravariantFunctor UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.Examples.Cofunctormap UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Sigma UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat