proposition: Lemma NR_to_hr_abs : ∏ x : NonnegativeReals × NonnegativeReals, hr_abs (NR_to_hr x) <= maxNonnegativeReals (pr1 x) (pr2 x).
proof: Proof. intros x. unfold hr_abs. rewrite hr_to_NRpos_NR_to_hr, hr_to_NRneg_NR_to_hr. apply maxNonnegativeReals_le. - eapply istrans_leNonnegativeReals, maxNonnegativeReals_le_l. now apply minusNonnegativeReals_le. - eapply istrans_leNonnegativeReals, maxNonnegativeReals_le_r. now apply minusNonnegativeReals_le. 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