Definition bind {A B} (aopt: option A) (f: A -> option B): option B :=
match aopt with None => None | Some a => f a end.
Section CombineList.
Variable A: Type.
Variable f: A -> A -> A.
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_Zlength: forall xs ys zs,
combinelist xs ys = Some zs -> Zlength zs = Zlength xs /\ Zlength ys = Zlength xs.