Definition opcleaving_of_opcleaving_opcartesian_2cell_is_pointwise_opcartesian : is_opcartesian (pr11 αα x xx). Proof. refine (transportb is_opcartesian opcleaving_of_opcleaving_opcartesian_2cell_is_pointwise_opcartesian_path _). use is_opcartesian_transportf. use is_opcartesian_comp_disp. - apply pointwise_opcartesian_lift_data_pointwise_opcartesian. - exact (is_opcartesian_z_iso_disp (disp_bicat_of_opcleaving_disp_invertible_2cell_pointwise_inv _ _ (pr2 (is_opcartesian_2cell_unique_iso Hαα pointwise_opcartesian_lift_data_is_opcartesian)) xx)). 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.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.Core.Examples.BicatOfUnivCats. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Opposite. 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.DispBicatOfDispCats.