Definition directed_set_all_inl_or_all_inr : (∀ (i : D), ∃ (x : X), D i = inl x) ∨ (∀ (i : D), ∃ (y : Y), D i = inr y).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous.