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_unique : forall {R : ConstructiveReals} (Un:nat -> CRcarrier R) (l1 l2:CRcarrier R), series_cv Un l1 -> series_cv Un l2 -> l1 == l2.