Proposition is_strongly_maximal_cotransitive_apartness {X : dcpo} (CX : continuous_dcpo_struct X) {x y z : X} (Hz : is_strongly_maximal z) (p : x # y) : x # z ∨ y # z. Proof. refine (is_sharp_cotransitive_apartness CX _ p). apply is_sharp_is_strongly_maximal. exact Hz. 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.Core.IntrinsicApartness. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous. Require Import UniMath.OrderTheory.DCPOs.Basis.Basis. Require Import UniMath.OrderTheory.DCPOs.Elements.Sharp.