Ltac coinductive_case CIH :=
    apply W_tl; simpl in *; auto;
    apply CIH; simpl in *; auto.

Theorem locking_clients_eventually_receive_lock_lb : 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 (InputLock c)) s -> eventually (now (occurred (MsgLocked c))) s.