Definition disp_cell_unit_bicat_univalent_2 (HC : is_univalent_2_1 C) (HDP : ∏ (a b : C) (f : a --> b) (aa : D a) (bb : D b), isaprop (aa -->[ f] bb)) (Dset : ∏ (a : C), isaset (D a)) (inv : ∏ (a : C) (aa bb : disp_cell_unit_bicat a), (aa -->[ id₁ a ] bb × bb -->[ id₁ a ] aa) → aa = bb) : disp_univalent_2 disp_cell_unit_bicat. Proof. split. - apply disp_cell_unit_bicat_univalent_2_0; assumption. - apply disp_cell_unit_bicat_univalent_2_1; assumption. 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.