Definition pb_disc_sopfib_mor_preserves_opcartesian : mor_preserves_opcartesian φ χ mor_of_pb_disc_sopfib_mor. Proof. use mor_preserves_opcartesian_pb_ump_mor_alt. intros z h₁ h₂ β Hβ. use (is_opcartesian_2cell_sopfib_precomp _ (_ ◃ ζ)). - exact ((β ▹ _) • (_ ◃ ζ)). - apply Hp. exact Hζ. - use vcomp_is_opcartesian_2cell_sopfib. + exact (from_pb_opcartesian Hφ (pr1 Hp) _ Hβ). + apply Hp. exact Hζ. - abstract (rewrite vcomp_whisker ; 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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Discreteness. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderPullback. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayMapBicatSlice. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Import PullbackFunctions.Notations.