Definition sfib_disp_map_bicat (B : bicat_with_pb) : disp_map_bicat B. Proof. use make_disp_map_bicat_with_pb. - exact (sfib_subbicat B). - intros pb x y z f g p₁ p₂ γ q Hpb. split. + exact (pb_of_sfib Hpb q). + exact (mor_preserves_cartesian_pb_pr1 Hpb q). - intros ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? H₁ H₂ H₃. apply mor_preserves_cartesian_pb_ump_mor. exact H₃. 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.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. 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.ContainsAdjEquiv. Require Import UniMath.Bicategories.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderPullback. Require Import UniMath.Bicategories.Morphisms.Properties.FromInitial. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Limits.Pullbacks.