proposition: Lemma CRdistance_triangle : forall (x y z : CR), CRdistance x z <= CRdistance x y + CRdistance y z.
proof: Proof. intros. unfold CRdistance. setoid_replace (x-z) with (x-y + (y-z)) by (unfold canonical_names.equiv, msp_Equiv; ring). apply CRabs_triangle. 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