proposition: Lemma series_cv_nonneg : forall {R : ConstructiveReals} (u : nat -> CRcarrier R) (s : CRcarrier R), (forall n:nat, 0 <= u n) -> series_cv u s -> 0 <= s.
proof: Proof. intros. apply (CRle_trans 0 (CRsum u 0)). - apply H. - apply (growing_ineq (CRsum u)). + intro n. simpl. rewrite <- CRplus_0_r. apply CRplus_le_compat. * rewrite CRplus_0_r. apply CRle_refl. * apply H. + apply H0. Qed.
imports: QArith Qabs ConstructiveReals ConstructiveRealsMorphisms ConstructiveAbs ConstructiveLimits