Proof using.
intros.
pose proof decomposition_invariant.
find_apply_lem_hyp inductive_invariant_true_in_reachable.
unfold true_in_reachable in *. apply H1; auto.
Qed.

(* Specifications: *)
Lemma locks_correct_invariant :
forall st,
reachable step_async step_async_init st ->
locks_correct (nwState st).
Lemma locks_correct_invariant :
forall st,
reachable step_async step_async_init st ->
locks_correct (nwState st).