Definition disp_univalent_2_0_slice (HB : is_univalent_2_1 B) : disp_univalent_2_0 slice_disp_bicat. Proof. use fiberwise_univalent_2_0_to_disp_univalent_2_0. intros x f g. use weqhomot. - exact (slice_inv2cell_weq_disp_adj_equiv HB f g ∘ make_weq _ (HB _ _ f g))%weq. - abstract (intro p ; cbn in p ; induction p ; use subtypePath ; [ intro ; apply (isaprop_disp_left_adjoint_equivalence _ _ HB disp_univalent_2_1_slice) | ] ; use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; cbn ; apply id2_left). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.