Definition bind {A B} (aopt: option A) (f: A -> option B): option B :=
  match aopt with None => None | Some a => f a end.Fixpoint combinelist xs ys :=
  match xs, ys with
    nil, nil => Some nil
  | (u::us),(v::vs) => bind (combinelist us vs) (fun l => Some (f u v :: l))
  | _, _ => None
  end.

Lemma combinelist_char_nth: forall xs ys l, combinelist xs ys = Some l -> forall i d, (0 <= i < length l)%nat -> nth i l d = f (nth i xs d) (nth i ys d).