proposition: Proposition less_than_dcpo_lub {X : dcpo} (D : directed_set X) (x : X) (i : D) (H : x ⊑ D i) : x ⊑ ⨆ D.
proof: Proof. exact (trans_PartialOrder X H (is_least_upperbound_is_upperbound (is_least_upperbound_dcpo_lub D) i)). Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets UniMath.OrderTheory.DCPOs.Core.DirectedSets