Proposition is_monotone_scott_continuous_map {X Y : dcpo} (f : scott_continuous_map X Y) {x₁ x₂ : X} (p : x₁ ⊑ x₂) : f x₁ ⊑ f x₂. Proof. exact (pr12 f x₁ x₂ p). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Core.IntrinsicApartness.