Lemma DAG_disp_univalent_2_0 : disp_univalent_2_0 DAG_disp_bicat. Proof. intros C1 C2 p dag1 dag2. use fiberwise_univalent_2_0_to_disp_univalent_2_0. intros C udag1 udag2. apply isweqimplimpl. - intro a. apply dagger_equality. repeat (apply funextsec ; intro). apply (pr1 a _). - intro ; apply isaset_dagger. - intro a. apply (isaprop_disp_adjoint_equivalence_cell_unit_bicat a) ; apply isaprop_is_dagger_functor. 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DaggerCategories.Categories. Require Import UniMath.CategoryTheory.DaggerCategories.Functors. Require Import UniMath.CategoryTheory.DaggerCategories.Transformations. Require Import UniMath.CategoryTheory.DaggerCategories.Unitary. Require Import UniMath.CategoryTheory.DaggerCategories.Univalence. Require Import UniMath.CategoryTheory.DaggerCategories.FunctorCategory. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat.