Definition dcpo_not_specialization {X : dcpo} (x y : X) : hProp := (∃ (P : X → hProp), is_scott_open P ∧ P x ∧ ¬(P y))%logic.
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.Basis.Continuous.