proposition: Proposition scott_continuous_lub_map_is_least_upperbound : is_least_upperbound (scott_continuous_map_PartialOrder X Y) D scott_continuous_lub_map.
proof: Proof. split. - intros i x. use less_than_dcpo_lub. + exact i. + apply refl_dcpo. - intros f Hf x ; cbn. unfold pointwise_lub. use dcpo_lub_is_least. intro i ; cbn. exact (Hf i x). 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 UniMath.OrderTheory.DCPOs.Core.FubiniTheorem UniMath.OrderTheory.DCPOs.Core.CoordinateContinuity UniMath.OrderTheory.DCPOs.Examples.BinaryProducts