proposition: Proposition is_sharp_is_strongly_maximal {X : dcpo} {x : X} (Hx : is_strongly_maximal x) : is_sharp x.
proof: Proof. intros u v p. specialize (Hx u v p). revert Hx. use factor_through_squash. { apply propproperty. } intro H. induction H as [ q | q ]. - exact (hinhpr (inl q)). - refine (hinhpr (inr _)). apply is_hausdorff_separated_not_le. exact 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 UniMath.OrderTheory.DCPOs.Basis.Basis UniMath.OrderTheory.DCPOs.Elements.Sharp