Definition continuous_struct_from_basis {X : dcpo} (B : dcpo_basis X) : continuous_dcpo_struct X. Proof. intro x. refine (directed_set_from_basis B x ,, _ ,, _). - intro i. exact (pr2 i). - apply is_least_upperbound_basis. 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.