Proof using.
intros.
find_apply_lem_hyp InputLock_Lock; auto.
destruct s.
simpl in *.
eauto using E_next, Lock_in_network_eventually_MsgLock,
lb_step_execution_invar, weak_fairness_invar.
Qed.

Lemma Nth_snoc :
forall A (l : list A) x,
Nth (l ++ [x]) (length l) x.