proposition: Lemma hr_mult_lecompat_r : ∏ x y z : hr_commring, hr_le_rel 0%ring x -> hr_le_rel y z -> hr_le_rel (x * y)%ring (x * z)%ring.
proof: Proof. intros x y z. rewrite !(ringcomm2 _ x). apply hr_mult_lecompat_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