proposition: Proposition compact_approximating_family_way_below (x : X) (i : compact_approximating_family x) : compact_approximating_family x i ≪ x.
proof: Proof. refine (trans_way_below_le (is_compact_approximating_family x i) _). exact (pr122 (AX x) i). Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.WayBelow UniMath.OrderTheory.DCPOs.Basis.Continuous