Definition disp_map_is_cartesian_2cell_sfib_to_is_cartesian_2cell_cell : hh ==>[ γ ] ss₁. Proof. use make_disp_map_bicat_cell. - use (is_cartesian_2cell_sfib_factor _ Hαα (pr1 γα)). + exact ((pr22 hh)^-1 • (_ ◃ γ) • pr22 ss₁). + abstract (rewrite !vassocl ; use vcomp_move_L_pM ; [ is_iso | ] ; refine (pr2 γα @ _) ; rewrite <- lwhisker_vcomp ; rewrite !vassocl ; apply maponpaths ; exact (!(pr2 αα))). - abstract (rewrite is_cartesian_2cell_sfib_factor_over ; rewrite !vassocr ; rewrite vcomp_rinv ; rewrite id2_left ; apply idpath). 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.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayMapBicatToDispBicat. Require Import UniMath.Bicategories.Limits.Pullbacks.