Definition directed_set_from_basis (B : dcpo_basis) (x : X) : directed_set X. Proof. use make_directed_set. - exact (basis_below_element B x). - exact (basis_below_map B x). - exact (is_directed_basis B x). Defined.
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. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous. Section ScottContinuousFromBasis. End ScottContinuousFromBasis.