Definition is_univalent_2_dirprod_bicat (HC : is_univalent_2_1 C) (HD1 : disp_univalent_2 D1) (HD2 : disp_univalent_2 D2) : disp_univalent_2 disp_dirprod_bicat. Proof. split. - apply is_univalent_2_0_dirprod_bicat; assumption. - apply is_univalent_2_1_dirprod_bicat. * exact (pr2 HD1). * exact (pr2 HD2). 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.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.