Definition all_inl_directed_set_to_left : directed_set X. Proof. use make_directed_set. - exact D. - exact all_inl_directed_set_map. - exact is_directed_all_inl_directed_set_to_left. Defined.
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.