End APPEND.
Section INQUEUE_APPEND.
Variable data : Set.

Lemma not_in_q_shuffle1 :
forall (m1 m2 : data) (q3 q4 : queue data),
~ In_queue data m2 (input data m1 (append data q3 q4)) ->
~ In_queue data m2 (append data q3 (input data m1 q4)).