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

(**********)
Lemma cv_cauchy_1 :
forall An:nat -> R,
{ l:R | Un_cv (fun N:nat => sum_f_R0 An N) l } ->
Cauchy_crit_series An.