proposition: Lemma Dcuts_minus_eq_zero: ∏ x y : Dcuts, x <= y -> Dcuts_minus x y = 0.
proof: Proof. intros X Y Hxy. apply Dcuts_eq_is_eq ; intros r ; split. - apply hinhuniv ; intros x. apply_pr2 (plusNonnegativeRationals_ltcompat_r (pr1 x)). rewrite islunit_zeroNonnegativeRationals. apply (pr2 (pr2 x)). left ; simple refine (Hxy _ _). exact (pr1 (pr2 x)). - intro H. now apply fromempty ; apply (Dcuts_zero_empty r). 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