Definition directed_set_point_map (i : D) : Y x. Proof. refine (transportf Y _ (pr2 (D i))). abstract (assert (h := H i) ; revert h ; use factor_through_squash ; [ apply setproperty | ] ; intro p ; exact (base_paths _ _ (pr2 p))). 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.