proposition: Proposition is_strict_scott_continuous_prodtofun {W X Y : hSet} {DW : dcppo_struct W} {DX : dcppo_struct X} {DY : dcppo_struct Y} {f : W → X} (Hf : is_strict_scott_continuous DW DX f) {g : W → Y} (Hg : is_strict_scott_continuous DW DY g) : is_strict_scott_continuous DW (prod_dcppo_struct DX DY) (prodtofuntoprod (f ,, g)).
proof: Proof. split. - exact (is_scott_continuous_prodtofun Hf Hg). - use pathsdirprod. + apply Hf. + apply Hg. 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