proposition: Proposition is_strict_scott_continuous_dirprod_pr1 {X Y : hSet} (DX : dcppo_struct X) (DY : dcppo_struct Y) : is_strict_scott_continuous (prod_dcppo_struct DX DY) DX dirprod_pr1.
proof: Proof. split. - apply is_scott_continuous_dirprod_pr1. - apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.PointedPosets UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous UniMath.OrderTheory.DCPOs.Core.ScottTopology UniMath.OrderTheory.DCPOs.Core.WayBelow UniMath.OrderTheory.DCPOs.Basis.Basis UniMath.OrderTheory.DCPOs.Basis.Continuous UniMath.OrderTheory.DCPOs.Elements.Maximal