proposition: Proposition is_scott_continuous_pr1_sub : is_scott_continuous sub_dcpo X pr1.
proof: Proof. use make_is_scott_continuous. - exact (is_monotone_pr1_sub X P). - cbn. intro. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous