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).