Definition disp_fullsubbicat_univalent_2_1 : disp_univalent_2_1 disp_fullsubbicat. Proof. apply fiberwise_local_univalent_is_univalent_2_1. intros x y f xx yy ff gg. use isweqimplimpl. - intros. apply isapropunit. - apply isasetaprop. exact isapropunit. - simple refine (isaprop_total2 (_ ,, _) (λ η , _ ,, _)). + exact isapropunit. + simpl. apply (@isaprop_is_disp_invertible_2cell C disp_fullsubbicat _ _ _ _ (id2_invertible_2cell f)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. 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.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat.