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_remainder : forall {R : ConstructiveReals} (u : nat -> CRcarrier R) (s sAbs : CRcarrier R) (n : nat), series_cv u s -> series_cv (fun n => CRabs R (u n)) sAbs -> CRabs R (CRsum u n - s) <= sAbs - CRsum (fun n => CRabs R (u n)) n.