proposition: Lemma Rap_Rlt: ∏ x y : Reals, x ≠ y <-> (x < y) ⨿ (y < x).
proof: Proof. exact hr_ap_lt. Qed.
imports: UniMath.Algebra.Groups UniMath.Foundations.Preamble UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.Sets UniMath.RealNumbers.NonnegativeRationals UniMath.RealNumbers.NonnegativeReals