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.