Proposition way_below_elem {X : dcpo} {x y : X} (p : x ≪ y) (D : directed_set X) (HD : y ⊑ ⨆ D) : ∃ (i : D), x ⊑ D i. Proof. exact (p D HD). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics.