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_abs_cv : forall {R : ConstructiveReals} (u : nat -> CRcarrier R) (cau : CR_cauchy R (CRsum (fun n => CRabs R (u n)))), series_cv u (let (l,_):= series_cv_abs u cau in l).