Section APPEND.
Variable data : Set.
Fixpoint append (q : queue data) : queue data -> queue data :=
fun q2 : queue data =>
match q with
| empty => q2
| input d q' => input data d (append q' q2)
end.

Lemma append_first_out :
forall (q1 : queue data) (d : data),
first_out data (append q1 (input data d (empty data))) = q1.