proposition: Lemma hr_opp_minus : ∏ x y : hr_commring, (x - y = - ((- x) - (- y)))%ring.
proof: Proof. intros x y. rewrite <- (hr_to_NR_bij x), <- (hr_to_NR_bij y). rewrite !NR_to_hr_opp, !NR_to_hr_plus, NR_to_hr_opp ; simpl. reflexivity. 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