Definition is_closed_under_lub (P : X → hProp) : hProp := (∀ (D : directed_set X), (∀ (i : D), P (D i)) ⇒ P(⨆ D))%logic.
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.Basis.Continuous.