Proof using.
intros.
unfold get_op_output_keys.
apply filterMap_NoDup_inj; auto.
intros.
repeat break_match; try discriminate.
subst. congruence.
Qed.

Lemma get_op_output_keys_complete :
forall xs k,
In (O k) xs ->
In k (get_op_output_keys xs).