proposition: Lemma hr_plus_ltcompat_r : ∏ x y z : hr_commring, hr_lt_rel y z <-> hr_lt_rel (x + y)%ring (x + z)%ring.
proof: Proof. intros x y z. rewrite !(ringcomm1 _ x). apply hr_plus_ltcompat_l. 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