Definition is_opcartesian_2cell_sopfib_to_is_opcartesian_2cell_cell : ss₂ ==>[ γ ] hh. Proof. cbn in *. use make_disp_2cell_cod. - use (is_opcartesian_2cell_sopfib_factor _ Hαα (pr1 γα)). + exact ((pr2 ss₂)^-1 • (_ ◃ γ) • pr2 hh). + abstract (use (vcomp_lcancel (pr12 ss₁)) ; [ apply (pr2 ss₁) | ] ; rewrite !vassocr ; rewrite !(pr2 γα) ; apply maponpaths_2 ; rewrite <- lwhisker_vcomp ; apply maponpaths_2 ; rewrite (pr2 αα) ; rewrite !vassocl ; rewrite vcomp_rinv ; rewrite id2_right ; apply idpath). - abstract (unfold coherent_homot ; 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.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. 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.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Core.Examples.OneTypes. 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.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.OneTypesLimits.