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 case_append_right :
forall (E : Set) (x y : E) (q1 q2 : queue data) (d : data),
match append q1 (input data d q2) with
| empty => x
| input _ _ => y
end = y.