proposition: Proposition least_fixpoint_scott_continuous_map_is_least_fixpoint {X : dcppo} (f : scott_continuous_map X X) : pr1 (least_fixpoint_scott_continuous_map X) f = least_fixpoint f.
proof: Proof. use antisymm_dcpo. - use dcpo_lub_is_least. intro i ; cbn in i. use less_than_dcpo_lub. + exact i. + rewrite <- least_fixpoint_scott_continuous_map_is_least_fixpoint_on_N. apply refl_dcpo. - use dcpo_lub_is_least. intro i ; cbn in i. use less_than_dcpo_lub. + exact i. + rewrite <- least_fixpoint_scott_continuous_map_is_least_fixpoint_on_N. apply refl_dcpo. 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