Definition cond_positivity (x:R) : bool :=
  match Rle_dec 0 x with
    | left _ => true
    | right _ => false
  end.

Lemma continuity_seq : forall (f:R -> R) (Un:nat -> R) (l:R), continuity_pt f l -> Un_cv Un l -> Un_cv (fun i:nat => f (Un i)) (f l).