proposition: Proposition scott_continuous_map_coordinates : scott_continuous_map (X × Y) Z.
proof: Proof. refine (f ,, _). use is_scott_continuous_chosen_lub. - exact scott_continuous_map_coordinates_monotone. - intros I D HD. exact (scott_continuous_map_coordinates_lub (I ,, D ,, HD)). Defined.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous UniMath.OrderTheory.DCPOs.Core.FubiniTheorem UniMath.OrderTheory.DCPOs.Examples.BinaryProducts