proposition: Lemma psfunctor_idtoiso {x y : C} {f g : x --> y} (p : f = g) (xx : pr1 (F x)) : pr1 (##F p) xx = idtoiso (maponpaths (λ h, pr1 (#F h) xx) p).
proof: Proof. induction p ; cbn. refine (_ @ nat_trans_eq_pointwise (psfunctor_id2 F _) xx). refine (maponpaths (λ h, h xx) _). do 2 apply maponpaths. 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