Definition cod_disp_univalent_2_1 (HB_2_1 : is_univalent_2_1 B) : disp_univalent_2_1 (cod_disp_bicat B). Proof. use fiberwise_local_univalent_is_univalent_2_1. intros c₁ c₂ f φ₁ φ₂ ψ₁ ψ₂. use weqhomot. - exact (cod_invertible_2_cell_weq_disp_invertible ∘ weqtotal2 (make_weq _ (HB_2_1 _ _ _ _)) cod_2cell_path ∘ total2_paths_equiv _ _ _)%weq. - intro p. induction p. use subtypePath. { intro ; apply isaprop_is_disp_invertible_2cell. } use subtypePath. { intro ; apply B. } apply idpath. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering. 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.Morphisms.Adjunctions. 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.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.OneTypes. 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.DisplayedBicats.Examples.Trivial. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma.