(* 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.