Proof using.
intros.
invc H; simpl in *.
- unfold network_invariant in *. simpl.
find_apply_lem_hyp PB_net_defn'.
workhorse; auto; intuition eauto.
- unfold network_invariant in *. simpl.
find_apply_lem_hyp PB_input_handler_defn.
workhorse; auto; intuition eauto.
Qed.

Lemma network_invariant_init :
network_invariant step_async_init.