Proof using.
induction l; intros; simpl in *; intuition.
apply op_equiv_trans with (l2 := (a :: O k :: l)).
- eauto 10.
- destruct a.
+ eauto 6 using good_op_move_neq_IO, op_equivalent_refl.
+ eauto 6 using good_op_move_OO, op_equivalent_refl.
Qed.

Lemma op_equiv_app_tail :
forall l xs ys,
op_equivalent xs ys ->
op_equivalent (xs ++ l) (ys ++ l).