proposition: Lemma minusNonnegativeRationals_eq_zero: ∏ x y : NonnegativeRationals, x <= y -> x - y = 0.
proof: Proof. intros x y Hle. unfold minusNonnegativeRationals, hnnq_minus. generalize (hqgthorleh (pr1 x) (pr1 y)). apply coprod_rect ; intros H. - apply fromempty. exact (Hle H). - reflexivity. Qed.
imports: UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders UniMath.RealNumbers.Sets UniMath.RealNumbers.Fields UniMath.Algebra.DivisionRig UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim