Definition disp_map_is_opcartesian_2cell_sopfib_to_is_opcartesian_2cell_cell : ss₂ ==>[ γ ] hh. Proof. use make_disp_map_bicat_cell. - use (is_opcartesian_2cell_sopfib_factor _ Hαα (pr1 γα)). + exact ((pr22 ss₂)^-1 • (_ ◃ γ) • pr22 hh). + abstract (use (vcomp_lcancel (pr22 ss₁)) ; [ apply (pr22 ss₁) | ] ; rewrite !vassocr ; refine (pr2 γα @ _) ; apply maponpaths_2 ; rewrite <- lwhisker_vcomp ; apply maponpaths_2 ; refine (!_) ; refine (maponpaths (λ z, z • _) (pr2 αα) @ _) ; rewrite !vassocl ; rewrite vcomp_rinv ; rewrite id2_right ; apply idpath). - abstract (rewrite is_opcartesian_2cell_sopfib_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.