Definition intersection_is_contravariant {B : bicat} {D₁ D₂ : disp_map_bicat B} (HD₁ : is_contravariant_disp_map_bicat D₁) (HD₂ : is_contravariant_disp_map_bicat D₂) : is_contravariant_disp_map_bicat (intersection_disp_map_bicat D₁ D₂). Proof. split. - intros x y f Hf. apply HD₁. apply Hf. - intros e₁ e₂ b₁ b₂ p₁ p₂ fe. split. + intro H. apply HD₁. apply H. + intro H. split. * apply HD₁. apply H. * apply HD₂. apply H. 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.