Proof using.
induction l; intros; simpl in *; intuition.
rewrite get_op_input_keys_defn.
pose proof H a. concludes. break_exists. subst.
auto.
Qed.

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