Proposition is_strongly_maximal_tight_apartness {X : dcpo} (CX : continuous_dcpo_struct X) {x y : X} (Hx : is_strongly_maximal x) (Hy : is_strongly_maximal y) (p : ¬(x # y)) : x = y. Proof. refine (is_sharp_tight_apartness CX _ _ p). - apply is_sharp_is_strongly_maximal. exact Hx. - apply is_sharp_is_strongly_maximal. exact Hy. 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.