proposition: Lemma CRabs_triangle : forall (x y : CR), CRabs (x+y) <= CRabs x + CRabs y.
proof: Proof. intros. apply CRabs_AbsSmall. split. 2: apply CRplus_le_compat; apply CRle_abs. rewrite CRopp_plus_distr. apply CRplus_le_compat; apply CRopp_le_cancel; rewrite CRopp_opp; rewrite <- CRabs_opp; apply CRle_abs. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QposMinMax CoRN.reals.fast.CRArith CoRN.model.metric2.Qmetric Coq.QArith.Qabs CoRN.model.totalorder.QMinMax CoRN.logic.Stability