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_symm (C: forall a b, f a b = f b a): forall xs ys, combinelist xs ys = combinelist ys xs.