proposition: Proposition lub_post_fixpoint {X : dcpo} (f : monotone_function X X) (D : directed_set X) (HD : ∏ (d : D), D d ⊑ f (D d)) : ⨆ D ⊑ f (⨆ D).
proof: Proof. use dcpo_lub_is_least. intro d. refine (trans_dcpo (HD d) _). apply f. use less_than_dcpo_lub. - exact d. - apply refl_dcpo. Qed.
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.Examples.Products UniMath.OrderTheory.DCPOs.Examples.SubDCPO