Proposition disp_psfunctor_iso_invmap_2_id2 {x y : B₁} {f : x --> y} {xx : D₁ x} {yy : D₁ y} {ff : xx -->[ f ] yy} (p : id₂ (# F f) = ## F (id₂ f)) : disp_psfunctor_iso_invmap_2 (transportf (λ z, _ ==>[ z ] _) p (disp_id2 (disp_psfunctor_mor D₁ D₂ F FF ff))) = disp_id2 _. Proof. refine (_ @ disp_psfunctor_iso_invmap_2_eq_2 (disp_id2 ff)). apply maponpaths. rewrite (disp_psfunctor_id2 _ _ _ FF (pr2 FF)). unfold transportb. apply maponpaths_2. apply cellset_property. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.DispTransportLaws.