Proof using.
intros.
simpl.
repeat break_match; auto;
exfalso; eauto using op_equiv_ack_op_lr, op_equiv_ack_op_rl.
Qed.

Lemma IR_equiv_AAOF_II_neq :
forall xs ys target k k',
k <> k' ->
op_equivalent xs ys ->
IR_equivalent (acknowledge_all_ops_func xs target)
(acknowledge_all_ops_func ys target) ->
IR_equivalent (acknowledge_all_ops_func (I k :: I k' :: xs) target)
(acknowledge_all_ops_func (I k' :: I k :: ys) target).