Definition series_cv_abs {R : ConstructiveReals} (u : nat -> CRcarrier R)
  : CR_cauchy R (CRsum (fun n => CRabs R (u n)))
    -> { l : CRcarrier R & series_cv u l }.

Lemma series_cv_plus : forall {R : ConstructiveReals} (u v : nat -> CRcarrier R) (s t : CRcarrier R), series_cv u s -> series_cv v t -> series_cv (fun n => u n + v n) (s + t).