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 input_append :
forall (d : data) (q1 q2 : queue data),
input data d (append q1 q2) = append (input data d q1) q2.