Proof using.
unfold good_op_move.
intuition congruence.
Qed.

(* Specifications: *)
Lemma good_op_move_OO :
forall k k',
good_op_move (O k) (O k').
Lemma op_equivalent_all_Is_O :
forall l k,
(forall k', In (I k') l -> k <> k') ->
op_equivalent (l ++ [O k]) (O k :: l).