Definition disp_cell_unit_bicat_univalent_2_1 (H : ∏ (a b : C) (f : a --> b) (aa : D a) (bb : D b), isaprop (aa -->[ f] bb)) : disp_univalent_2_1 disp_cell_unit_bicat. Proof. intros a b f g p aa bb ff gg. use isweqimplimpl. - cbn in *. intros. apply H. - apply isasetaprop. exact (H a b g aa bb). - simple refine (isaprop_total2 (_ ,, _) (λ η , _ ,, _)). + exact isapropunit. + apply (@isaprop_is_disp_invertible_2cell C disp_cell_unit_bicat). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Propositions. 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.