proposition: Proposition least_fixpoint_scott_continuous_map_is_least_fixpoint_on_N {X : dcppo} (f : scott_continuous_map X X) (n : ℕ) : pr1 (least_fixpoint_scott_continuous_map_on_N n) f = bot_iteration_directed_set f n.
proof: Proof. induction n as [ | n IHn ]. - apply idpath. - refine (_ @ maponpaths _ IHn). simpl ; unfold prodtofuntoprod ; simpl. apply (iterate_on_pt_scott_continuous_map_fun_pt n f). 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