Definition pb_of_sfib_cleaving_cell_is_cartesian_2cell_sfib : is_cartesian_2cell_sfib p₁ pb_of_sfib_cleaving_cell. Proof. apply to_pb_cartesian. refine (is_cartesian_eq _ (!(pb_ump_cell_pr1 H _ _ _ _ _)) _). use vcomp_is_cartesian_2cell_sfib. - apply invertible_is_cartesian_2cell_sfib. apply property_from_invertible_2cell. - apply internal_sfib_cleaving_is_cartesian. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Examples.OpCellBicatLimits. Section FromPBCartesian. End FromPBCartesian.