proposition: Lemma Dcuts_minus_bot : Dcuts_def_bot Dcuts_minus_val.
proof: Proof. intros r Hr q Hle. revert Hr ; apply hinhfun ; intros x. exists (pr1 x) ; split. - exact (pr1 (pr2 x)). - intros y Yy. apply istrans_le_lt_ltNonnegativeRationals with (r + y). + apply plusNonnegativeRationals_lecompat_r. exact Hle. + now apply (pr2 (pr2 x)). 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