proposition: Lemma Dcuts_plus_lecompat_l : ∏ x y z: Dcuts, (y <= z) <-> (Dcuts_plus y x <= Dcuts_plus z x).
proof: Proof. intros x y z. split. - intros H ; apply Dcuts_nlt_ge ; intro H0 ; apply (pr2 (Dcuts_nlt_ge _ _) H). now apply_pr2 (Dcuts_plus_ltcompat_l x). - intros H ; apply Dcuts_nlt_ge ; intro H0 ; apply (pr2 (Dcuts_nlt_ge _ _) H). now apply Dcuts_plus_ltcompat_l. 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