Definition message_delivered_label p l :=
    forall l' net net' tr,
      lb_step_async net l' net' tr ->
      In p (nwPackets net) ->
      ~ In p (nwPackets net') ->
      l = l'.

Lemma In_split_not_In : forall A (p : A) p' xs ys zs, In p (xs ++ p' :: ys) -> ~ In p (zs ++ xs ++ ys) -> p = p'.