(* Cauchy's criterion for series *)
Definition Cauchy_crit_series (An:nat -> R) : Prop :=
Cauchy_crit (fun N:nat => sum_f_R0 An N).

(* If (|An|) satisfies the Cauchy's criterion for series, then (An) too *)
Lemma cauchy_abs :
forall An:nat -> R,
Cauchy_crit_series (fun i:nat => Rabs (An i)) -> Cauchy_crit_series An.