proposition: Theorem is_least_fixpoint_least_fixpoint (x : X) (p : f x = x) : least_fixpoint ⊑ x.
proof: Proof. use dcpo_lub_is_least ; cbn. intro n. induction n as [ | n IHn ]. - apply is_min_bottom_dcppo. - rewrite <- p. exact (is_monotone_scott_continuous_map f IHn). 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.Examples.Fixpoints UniMath.OrderTheory.DCPOs.Examples.Exponentials UniMath.OrderTheory.DCPOs.Examples.BinaryProducts