proposition: Lemma ARabs_opp : forall x:AR, ARabs (-x) = ARabs x.
proof: Proof. intro x. apply (injective ARtoCR). pose proof (ARtoCR_preserves_abs (-x)). unfold cast in H5. rewrite H5. clear H5. pose proof (ARtoCR_preserves_abs x). unfold cast in H5. rewrite H5. rewrite (ARtoCR_preserves_opp x). apply CRabs_opp. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity Coq.QArith.Qabs CoRN.model.metric2.Qmetric CoRN.model.totalorder.QposMinMax CoRN.model.totalorder.QMinMax CoRN.reals.fast.CRabs CoRN.reals.faster.ARArith