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