Proof using.
intros.
eapply In_cons_2_3_neq.
- auto with *.
- intro. find_inversion. eauto using get_IR_input_keys_complete.
- discriminate.
Qed.

Lemma subseq_get_op_input_keys :
forall xs ys,
subseq xs ys ->
subseq (get_op_input_keys xs) (get_op_input_keys ys).