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_shift : forall {R : ConstructiveReals} (f : nat -> CRcarrier R) k l, series_cv (fun n => f (S k + n)%nat) l -> series_cv f (l + CRsum f k).