proposition: Lemma L1Norm_scale : forall q s, (L1Norm (QscaleS q ^@> s) == Qabs q * L1Norm s)%Q.
proof: Proof. intros q s. unfold L1Norm. rewrite -> Integral_scale. apply IntegralQ_wd. unfold StepF_eq. set (g:= st_eqS). set (q0 := (QscaleS q)). set (q1 := (QscaleS (Qabs q))). set (f:= ap (compose g (compose QabsS q0)) (compose q1 QabsS)). cut (StepFfoldProp (f ^@> s)). unfold f. evalStepF. tauto. apply StepFfoldPropForall_Map. intros a. apply: Qabs_Qmult. 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