Proposition dcpo_not_specialization_le {x y : X} (p : x ⊄ y) : ¬(x ⊑ y). Proof. intro q. revert p. use factor_through_squash. { apply isapropempty. } intros P. induction P as [ P [ HP [ Px Py ]]]. refine (Py _). exact (is_scott_open_upper_set HP Px q). Qed.
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.