proposition: Lemma hr_abs_opp : ∏ x : hr_ConstructiveField, hr_abs (- x)%ring = hr_abs x.
proof: Proof. intros x. unfold hr_abs. rewrite hr_to_NRpos_opp, hr_to_NRneg_opp. apply iscomm_maxNonnegativeReals. 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