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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
Require Export DistributedReferenceCounting.machine3.invariant0.
Require Export DistributedReferenceCounting.machine3.invariant1.
Require Export DistributedReferenceCounting.machine3.invariant2.
Unset Standard Proposition Elimination Names.
(* Where properties of rooted_fun are derived --> this should obviously be abstracted and given decent names *)
Section INVARIANT3.

Lemma sigma_rooted_fun1 :
forall (s s1 s2 : Site) (d : Message),
s2 <> owner ->
~ In s1 LS ->
~ In s2 LS ->
sigma_but Site owner eq_site_dec LS (fun s : Site => rooted_fun s s1 s2 d) =
0%Z.