proposition: Proposition is_monotone_pointwise_lub (x₁ x₂ : X) (p : x₁ ⊑ x₂) : pointwise_lub x₁ ⊑ pointwise_lub x₂.
proof: Proof. unfold pointwise_lub. use dcpo_lub_is_least ; cbn. intro i. use less_than_dcpo_lub. - exact i. - exact (is_monotone_scott_continuous_map (_ ,, pr2 (D i)) p). 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