proposition: Lemma InfiniteGeometricSum_correct' : forall (series:Stream Q) (a : Q) (apos : 0 <= a) (aone : a < 1), forall (Gs:GeometricSeries a series), (InfiniteGeometricSum apos aone Gs == IRasCR (series_sum _ (GeometricSeries_convergent apos aone Gs)))%CR.
proof: Proof. intros series a apos aone Gs. apply InfiniteGeometricSum_correct. intros; apply eq_reflexive. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.iso_CReals CoRN.reals.fast.CRAlternatingSum CoRN.reals.fast.CRGeometricSum CoRN.reals.fast.CRstreams CoRN.reals.fast.CRArith CoRN.reals.fast.CRIR Coq.QArith.Qabs Coq.QArith.Qpower CoRN.model.ordfields.Qordfield CoRN.reals.Q_in_CReals CoRN.model.metric2.Qmetric CoRN.model.totalorder.QMinMax CoRN.transc.ArTanH CoRN.reals.fast.CRarctan_small CoRN.tactics.Qauto CoRN.tactics.CornTac