Proof using.
intros.
apply filterMap_app.
Qed.

(* Specifications: *)
Lemma get_op_output_keys_app :
forall xs ys,
get_op_output_keys (xs ++ ys) = get_op_output_keys xs ++ get_op_output_keys ys.
Lemma get_op_input_keys_complete :
forall xs k,
In (I k) xs ->
In k (get_op_input_keys xs).