Definition is_lub_inaccessible (P : X → hProp) : hProp := (∀ (D : directed_set X), P(⨆ D) ⇒ ∃ (i : D), P(D i))%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.