End IN_Q_EFFECT.
Section CARD_EFFECT.
(* consequence sur le nombre *)

(* Specifications: *)
Lemma post_card_mess :
forall (m : Message) (s1 s2 : Site) (b : Bag_of_message),
card_mess m (Post_message m b s1 s2 s1 s2) = (card_mess m (b s1 s2) + 1)%Z.
Lemma diff_post_card_mess :
forall (m m' : Message) (s1 s2 s3 s4 : Site) (b : Bag_of_message),
m <> m' \/ s1 <> s3 \/ s2 <> s4 ->
card_mess m (Post_message m' b s3 s4 s1 s2) = card_mess m (b s1 s2).
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.
Lemma diff_collect_card_mess :
forall (m : Message) (s1 s2 s3 s4 : Site) (b : Bag_of_message),
first Message (b s1 s2) <> value Message m \/ s1 <> s3 \/ s2 <> s4 ->
card_mess m (Collect_message b s3 s4 s1 s2) = card_mess m (b s1 s2).