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.