Proof using.
set_up_net_handlers.
Qed.
Instance LockServ_Decompositition : Decomposition _ LockServ_MultiParams.
apply Build_Decomposition with (state_invariant := locks_correct)
(network_invariant := LockServ_network_invariant)
(network_network_invariant := LockServ_network_network_invariant);
simpl; intros; monad_unfold; repeat break_let; repeat find_inversion.
- auto using nwnw_sym.
- auto using locks_correct_init.
- eauto using locks_correct_input_handlers.
- unfold LockServ_network_invariant in *. intuition.
eauto using locks_correct_net_handlers.
- unfold LockServ_network_invariant in *.
intuition eauto using locks_correct_unlock_input_handlers_old,
locks_correct_locked_input_handlers_old.
- unfold LockServ_network_invariant in *.
intuition eauto using locks_correct_unlock_input_handlers_new,
locks_correct_locked_input_handlers_new.
- unfold LockServ_network_invariant in *.
intuition eauto using locks_correct_unlock_net_handlers_old,
locks_correct_locked_net_handlers_old.
- unfold LockServ_network_invariant in *.
intuition eauto using locks_correct_unlock_net_handlers_new,
locks_correct_locked_net_handlers_new.
- eauto using LockServ_nwnw_input_handlers_old_new.
- eauto using LockServ_nwnw_input_handlers_new_new.
- eauto using LockServ_nwnw_net_handlers_old_new.
- eauto using LockServ_nwnw_net_handlers_new_new.
Defined.

Theorem true_in_reachable_mutual_exclusion :
true_in_reachable step_async step_async_init (fun net => mutual_exclusion (nwState net)).