proposition: Lemma StepQSup_resp_le : forall x y, x <= y -> (StepQSup x <= StepQSup y)%Q.
proof: Proof. apply: StepF_ind2; auto. intros s s0 t t0 Hs Ht. rewrite -> Hs, Ht; auto. intros o s s0 t t0 H0 H1. unfold StepQ_le. rewriteStepF. intros [Hl Hr]. repeat rewrite StepQSup_glue. apply Qmax_le_compat; auto. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.structures.StepQsec CoRN.metric2.Prelength CoRN.model.metric2.L1metric CoRN.model.metric2.LinfMetricMonad 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