proposition: Lemma Dcuts_minus_le : ∏ x y, Dcuts_minus x y <= x.
proof: Proof. intros X Y r. apply hinhuniv ; intros x. apply is_Dcuts_bot with (1 := pr1 (pr2 x)). apply lt_leNonnegativeRationals. pattern r at 1 ; rewrite <- (isrunit_zeroNonnegativeRationals r). apply (pr2 (pr2 x)). now right. 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