proposition: Lemma ap_ltNonnegativeReals : ∏ x y : NonnegativeReals, x ≠ y <-> (x < y) ⨿ (y < x).
proof: Proof. now intros x y ; split. 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