proposition: Proposition irrefl_is_hausdorff_separated (x : X) : ¬(is_hausdorff_separated x x).
proof: Proof. use factor_through_squash. { apply isapropempty. } intros H. induction H as [ P₁ [ P₂ [ Px [ Px' H ]]]]. exact (H x (Px ,, Px')). Qed.
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