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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
Require Export DistributedReferenceCounting.machine1.invariant0.
Require Export DistributedReferenceCounting.machine1.invariant1.
Require Export DistributedReferenceCounting.machine1.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_fun11 :
forall (s1 s2 : Site) (l : list Site),
s2 <> owner ->
s1 <> owner ->
~ In s2 l ->
sigma_but Site owner eq_site_dec l (fun s : Site => rooted_fun s s1 s2 dec) =
0%Z.