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_nonneg : forall {R : ConstructiveReals}
(u : nat -> CRcarrier R) (s : CRcarrier R),
(forall n:nat, 0 <= u n) -> series_cv u s -> 0 <= s.