Proof using.
induction tr; intros; simpl in *; repeat break_match; subst; intuition.
Qed.

(* Specifications: *)
Lemma decomposition_reachable_nw_invariant :
forall st tr p,
step_async_star step_async_init st tr ->
In p (nwPackets st) ->
network_invariant (nwState st) p.
Lemma decomposition_reachable_nw_invariant :
forall st tr p,
step_async_star step_async_init st tr ->
In p (nwPackets st) ->
network_invariant (nwState st) p.