Definition is_univalent_2_1_dirprod_bicat (HD1 : disp_univalent_2_1 D1) (HD2 : disp_univalent_2_1 D2) : disp_univalent_2_1 disp_dirprod_bicat. Proof. intros a b f g p aa bb ff gg. use weqhomot. - exact (prod_idtoiso_2_1 p ff gg HD1 HD2). - intros q. induction p, q. use subtypePath. + intro. apply (@isaprop_is_disp_invertible_2cell C disp_dirprod_bicat). + reflexivity. 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.