Definition disp_univalent_2_1_along_iso : disp_univalent_2_1 D₁. Proof. use fiberwise_local_univalent_is_univalent_2_1. intros x y f xx yy ff gg. use weqhomot. - exact (disp_invertible_2cell_along_iso_weq ff gg ∘ make_weq _ (HD₂ _ _ _ _ (idpath (#F f)) (FF x xx) (FF y yy) _ _) ∘ make_weq _ (isweqonpathsincl _ (isinclweq _ _ _ (pr2 (disp_psfunctor_iso_mor_weq HF f xx yy))) ff gg))%weq. - abstract (intro p ; cbn in p ; induction p ; use subtypePath ; [ intro ; apply isaprop_is_disp_invertible_2cell | ] ; cbn ; refine (_ @ disp_psfunctor_iso_invmap_2_eq_2 HF _) ; apply maponpaths ; rewrite (disp_psfunctor_id2 _ _ _ FF (pr2 FF)) ; apply maponpaths_2 ; apply cellset_property). Defined.
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.