Definition pr2_disp_invertible_2cell {a b : C} {f : a --> b} {g : a --> b} (x : invertible_2cell f g) {aa : disp_dirprod_bicat a} {bb : disp_dirprod_bicat b} (ff : aa -->[ f ] bb) (gg : aa -->[ g ] bb) : disp_invertible_2cell x ff gg → disp_invertible_2cell x (pr2 ff) (pr2 gg). Proof. intros H. use tpair. - apply H. - refine (pr2_is_disp_invertible_2cell _ _ _). apply H. 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.