proposition: Lemma Dcuts_half_bot : Dcuts_def_bot Dcuts_half_val.
proof: Proof. intros r Hr q Hq. apply X_bot with (1 := Hr). eapply istrans_leNonnegativeRationals, plusNonnegativeRationals_lecompat_l, Hq. now apply plusNonnegativeRationals_lecompat_r, Hq. 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