Ltac start :=
    red; unfold append_entries_leaderLogs; intros;
    subst; simpl in *; find_higher_order_rewrite;
    update_destruct; subst; rewrite_update; eauto; simpl in *.Ltac prove_in :=
    match goal with
      | [ _ : nwPackets ?net = _,
              _ : In (?p : packet) _ |- _] =>
        assert (In p (nwPackets net)) by (repeat find_rewrite; do_in_app; intuition)
      | [ _ : nwPackets ?net = _,
              _ : pBody ?p = _ |- _] =>
        assert (In p (nwPackets net)) by (repeat find_rewrite; intuition)
    end.

Lemma findGtIndex_app_in_2 : forall l1 l2 e, sorted (l1 ++ l2) -> In e l2 -> exists l', findGtIndex (l1 ++ l2) (eIndex e) = l1 ++ l' /\ Prefix l' l2.