Proof using.
intros.
find_apply_lem_hyp MsgLock_in_queue_or_Locked; auto.
intuition.
- destruct s; simpl in *; eauto using E_next, E0.
- break_exists.
destruct s; simpl in *.
apply E_next.
eapply clients_get_lock_messages;
eauto using lb_step_execution_invar,
weak_fairness_invar.
find_apply_lem_hyp step_async_star_lb_step_execution; auto.
destruct s. simpl.
do 2 (find_apply_lem_hyp always_Cons; intuition).
Qed.

Lemma MsgLock_eventually_MsgLocked :
forall c s,
event_step_star step_async step_async_init (hd s) ->
lb_step_execution lb_step_async s ->
weak_fairness lb_step_async label_silent s ->
now (occurred (MsgLock c)) s ->
eventually (now (occurred (MsgLocked c))) s.