proposition: Lemma L1_is_MetricSpace : (is_MetricSpace L1Ball).
proof: Proof. split. - intros e H x. apply L1ball_refl, H. - apply: L1ball_sym. - apply: L1ball_triangle. - apply: L1ball_closed. - intros. unfold L1Ball, L1Distance in H. apply (Qle_trans _ (L1Norm (a-b))). apply L1Norm_nonneg. exact H. - intros. unfold L1Ball, L1Distance. unfold L1Ball, L1Distance in H. apply Qnot_lt_le. intro abs. contradict H; intro H. exact (Qle_not_lt _ _ H abs). Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QposMinMax CoRN.model.structures.StepQsec CoRN.metric2.UniformContinuity CoRN.metric2.Prelength CoRN.model.structures.OpenUnit Coq.QArith.QArith CoRN.model.totalorder.QMinMax Coq.QArith.Qabs CoRN.model.ordfields.Qordfield CoRN.model.metric2.Qmetric CoRN.algebra.COrdFields2 CoRN.tactics.CornTac