Definition pb_lift_2cell_factor : lift_2cell_factor DD hf σσ Lh Lh'. Proof. use iscontraprop1. - exact pb_lift_2cell_factor_unique. - simple refine (_ ,, _). + use make_disp_map_bicat_cell. * exact pb_lift_2cell_factor_cell. * abstract (etrans ; [ apply maponpaths ; apply (pb_ump_cell_pr2 Hpb) | ] ; rewrite !vassocr ; rewrite vcomp_rinv, id2_left ; apply idpath). + abstract (use subtypePath ; [ intro ; apply cellset_property | ] ; refine (transportf_disp_map_bicat_cell _ _ _ @ _) ; cbn ; etrans ; [ apply maponpaths_2 ; apply (pb_ump_cell_pr1 Hpb) | ] ; do 2 refine (vassocl _ _ _ @ _) ; apply maponpaths ; refine (_ @ id2_right _) ; apply maponpaths ; apply vcomp_linv). 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.