Definition disp_univalent_2_0_disp_end (HB : is_univalent_2_1 B) : disp_univalent_2_0 disp_end. Proof. intros x y p ex ey. induction p. use weqhomot. - exact (inv2cell_weq_disp_adj_equiv_disp_end HB ex ey ∘ make_weq _ (HB x x ex ey))%weq. - abstract (intro p ; induction p ; use subtypePath ; [ intro ; use (isaprop_disp_left_adjoint_equivalence _ _ HB) ; apply disp_univalent_2_1_disp_end | ] ; cbn ; rewrite id2_right ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.