proposition: Lemma hr_lt_le : ∏ X Y, hr_lt_rel X Y -> hr_le_rel X Y.
proof: Proof. intros x y. rewrite <- (hr_to_NR_bij x), <- (hr_to_NR_bij y). intro H. apply NR_to_hr_le. apply lt_leNonnegativeReals. apply_pr2 NR_to_hr_lt. exact H. 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