Definition good_op_move (x y : op) : Prop :=
    (forall k k', ~ (x = O k /\ y = I k')) /\
    (forall k, ~ (x = I k /\ y = O k)).

Lemma get_op_input_keys_preserves_NoDup : forall l, NoDup l -> NoDup (get_op_input_keys l).