proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.Initial UniMath.Bicategories.Core.Examples.Final UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.TransportLaws UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.DisplayedBicats.DispPseudofunctor UniMath.Bicategories.DisplayedBicats.DispTransportLaws