Definition closed_under_comp : UU := ∏ (e₁ e₂ e₃ b₁ b₂ b₃ : B) (p₁ : e₁ --> b₁) (p₂ : e₂ --> b₂) (p₃ : e₃ --> b₃) (fe : e₁ --> e₂) (ge : e₂ --> e₃), P₁ p₁ p₂ fe → P₁ p₂ p₃ ge → P₁ p₁ p₃ (fe · ge).
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.