Definition map_directed_set_from_basis (x : X) : directed_set Y. Proof. use make_directed_set. - exact (basis_below_element B x). - exact (λ i, f (pr1 i)). - exact (is_directed_map_from_basis 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.