proposition: Proposition is_sharp_tight_apartness {X : dcpo} (CX : continuous_dcpo_struct X) {x y : X} (Hx : is_sharp x) (Hy : is_sharp y) (p : ¬(x # y)) : x = y.
proof: Proof. use antisymm_dcpo. - use (is_sharp_to_le CX Hy). intro q. apply p. exact (hinhpr (inl q)). - use (is_sharp_to_le CX Hx). intro q. apply p. exact (hinhpr (inr q)). 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