proposition: Proposition is_fixpoint_least_fixpoint : f least_fixpoint = least_fixpoint.
proof: Proof. unfold least_fixpoint. rewrite scott_continuous_map_on_lub. use antisymm_dcpo. - use dcpo_lub_is_least. cbn ; intro i. use less_than_dcpo_lub. + exact (S i). + apply refl_dcpo. - use dcpo_lub_is_least. cbn ; intro i. use less_than_dcpo_lub. + exact i. + apply is_monotone_bot_iteration_map_S. 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