Proof using.
set_up_input_handlers.
destruct (pBody p) eqn:?.
- auto using locks_correct_unlock_sent_lock.
- now erewrite unlock_in_flight_all_clients_false in * by eauto.
- auto using locks_correct_unlock_sent_locked.
Qed.

Lemma locked_in_flight_all_clients_false :
forall sigma p,
pBody p = Locked ->
locks_correct_locked sigma p ->
locks_correct sigma ->
(forall c, held (sigma (Client c)) = false).