Section REDUCE_EFFECT.
Variable Message : Set.
Let Bag_of_message := Bag_of_Data Message.
Variable f : Message -> Z.

Lemma reduce_post_message :
forall (m : Message) (s1 s2 : Site) (b : Bag_of_message),
reduce Message f (Post_message Message m b s1 s2 s1 s2) =
(reduce Message f (b s1 s2) + f m)%Z.