Definition is_hausdorff_separated {X : dcpo} (x y : X) : hProp := ∃ (P₁ P₂ : scott_open_set X), P₁ x ∧ P₂ y ∧ are_disjoint P₁ P₂.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Core.IntrinsicApartness. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous. Require Import UniMath.OrderTheory.DCPOs.Basis.Basis. Require Import UniMath.OrderTheory.DCPOs.Elements.Sharp.