Proposition symmetric_intrinsic_apartness {x y : X} (p : x # y) : y # x. Proof. revert p. use factor_through_squash. { apply propproperty. } intros p. induction p as [ p | p ]. - exact (hinhpr (inr p)). - exact (hinhpr (inl p)). 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.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous.