Proposition bot_way_below {X : dcppo} (x : X) : ⊥_{X} ≪ x. Proof. intros D HD. assert (H := directed_set_el D). revert H. use factor_through_squash. { apply propproperty. } intro i. refine (hinhpr (i ,, _)). apply is_min_bottom_dcppo. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics.