Proposition is_scott_continuous_map_from_basis : is_scott_continuous (pr2 X) (pr2 Y) map_from_basis. Proof. use make_is_scott_continuous. - exact map_from_basis_monotone. - exact map_from_basis_lub. Qed.
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.