Proof using.
unfold get_op_input_keys.
intros.
eapply filterMap_In; eauto.
auto.
Qed.

(* Specifications: *)
Lemma get_op_input_keys_sound :
forall k l,
In k (get_op_input_keys l) ->
In (I k) l.
Lemma get_IR_output_keys_complete_U :
forall xs k,
In (IRU k) xs ->
In k (get_IR_output_keys xs).