proposition: Lemma istight_Dcuts_ap_rel : istight Dcuts_ap_rel.
proof: Proof. intros X Y Hap. apply Dcuts_eq_is_eq. intros r ; split ; revert r. - change (X <= Y). apply Dcuts_le_ngt_rel. intro Hlt ; apply Hap. now right. - change (Y <= X). apply Dcuts_le_ngt_rel. intro Hlt ; apply Hap. now left. Qed.
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