Proposition is_compact_approximating_family (x : X) (i : compact_approximating_family x) : is_compact_el (compact_approximating_family x i). Proof. exact (pr12 (AX x) i). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous.