Section ROOTED1.

Lemma sigma_rooted_collect_message :
forall (m : Message) (s0 s1 s2 : Site) (b : Bag_of_message),
first Message (b s1 s2) = value Message m ->
s0 <> owner ->
sigma_rooted s0 (Collect_message Message b s1 s2) =
(sigma_rooted s0 b - rooted_fun s0 s1 s2 m)%Z.