proposition: Proposition transportf_psfunctor_into_cat {C : category} {F : psfunctor (cat_to_bicat C^op) bicat_of_univ_cats} {x y : C} (f : x --> y) (yy : pr1 (F y)) {g h : x --> y} (p : g = h) (ff : pr1 (# F f) yy --> pr1 (# F g) yy) : transportf (λ z, pr1 (#F f) yy --> pr1 (#F z) yy) p ff = ff · pr1 (##F p) yy.
proof: Proof. induction p ; cbn. refine (!(id_right _) @ _). apply maponpaths. refine (!(nat_trans_eq_pointwise (psfunctor_id2 F _) _) @ _). refine (maponpaths (λ z, pr1 (##F z) yy) _). apply homset_property. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.IndexedCategories.IndexedCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.OppositeCategory.Core UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Discreteness UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Examples.DiscreteBicat UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor