fact: Definition Dcuts_ap_rel (X Y : Dcuts_set) : hProp := make_hProp ((X < Y) ⨿ (Y < X)) (isaprop_Dcuts_ap_rel X Y).
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals