proposition: Lemma Integral_resp_nonneg :forall x, (constStepF (0:QS)) <= x -> (0 <= (IntegralQ x))%Q.
proof: Proof. intros x. unfold StepQ_le. rewriteStepF. induction x. auto. rewriteStepF. intros [Hxl Hxr]. apply: plus_resp_nonneg; apply: mult_resp_nonneg; simpl; auto with *. 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