Definition global_mor_id : disp_invertible_2cell (id2_invertible_2cell (id₁ x)) (global_lift_mor (id_disp yy)) (id_disp _). Proof. simple refine (_ ,, _). + exact (cartesian_1cell_lift_2cell D _ (is_cartesian_mor_from_global_lift f yy) global_mor_id_cell _ (id_disp (global_lift f yy) ,, global_mor_id_factor)). + use (cartesian_1cell_lift_2cell_invertible D (is_cartesian_mor_from_global_lift f yy) _ _ _ (id_disp (global_lift f yy) ,, global_mor_id_factor)). exact (pr2 global_mor_id_cell). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Discreteness. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.FiberCategory. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Cartesians.