Definition pb_disc_sopfib_mor {x : B} {f g : hom x s} (α : f --> g) : disc_sopfib_slice HB x ⟦ pr1 (pb _ f) , pr1 (pb _ g) ⟧. Proof. simple refine (_ ,, (_ ,, tt) ,, _) ; cbn. - exact (mor_of_pb_disc_sopfib_mor α). - exact (pb_disc_sopfib_mor_preserves_opcartesian α). - exact (cell_of_pb_disc_sopfib_mor α). 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.