Section CARD_EFFECT.
(* consequence sur le nombre *)

Lemma collect_card_mess :
forall (m : Message) (s1 s2 : Site) (b : Bag_of_message),
first Message (b s1 s2) = value Message m ->
card_mess m (Collect_message b s1 s2 s1 s2) = (card_mess m (b s1 s2) - 1)%Z.