Proof using.
induction l; intros; simpl in *; intuition.
apply op_equiv_trans with (l2 := (a :: I k :: l)).
- auto.
- specialize (H a). concludes. break_exists. subst.
auto using op_equivalent_refl, good_op_move_II.
Qed.

Lemma good_op_move_neq_IO :
forall k k',
k <> k' ->
good_op_move (I k) (O k').