Definition intersection_arrow_subbicat_props {B : bicat} {D₁ D₂ : arrow_subbicat B} (HD₁ : arrow_subbicat_props D₁) (HD₂ : arrow_subbicat_props D₂) : arrow_subbicat_props (intersection_arrow_subbicat D₁ D₂). Proof. split. - intros x y f. apply isapropdirprod. + exact (pr1 HD₁ _ _ f). + exact (pr1 HD₂ _ _ f). - intros e₁ e₂ b₁ b₂ p₁ p₂ fe. apply isapropdirprod. + exact (pr2 HD₁ _ _ _ _ p₁ p₂ fe). + exact (pr2 HD₂ _ _ _ _ p₁ p₂ fe). 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.