proposition: Proposition approximating_family_lub (x : X) : ⨆ (approximating_family x) = x.
proof: Proof. use antisymm_dcpo. - use dcpo_lub_is_least. intro i. apply way_below_to_le. exact (approximating_family_way_below x i). - use (is_least_upperbound_is_least (pr22 (CX x))). apply is_least_upperbound_is_upperbound. apply is_least_upperbound_dcpo_lub. Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.WayBelow