Section CONTROL_POS.
(* preuves que ces decomptes sont positifs (ils sont fait dans Z) *)
Variable bom : Bag_of_message.
Remark ctrl_inc_pos : forall s0 s1 : Site, (ctrl_inc s0 s1 bom >= 0)%Z.
Remark ctrl_inc_strct_pos :
forall s0 s1 : Site,
In_queue Message (inc_dec s0) (bom s1 owner) -> (ctrl_inc s0 s1 bom > 0)%Z.
Remark sigma_ctrl_copy_pos :
forall s0 : Site, (sigma_ctrl_copy s0 bom >= 0)%Z.
Remark sigma_ctrl_dec_pos : forall s0 : Site, (sigma_ctrl_dec s0 bom >= 0)%Z.
Remark sigma_ctrl_inc_strct_pos :
forall s0 s1 : Site,
In_queue Message (inc_dec s0) (bom s1 owner) ->
(sigma_ctrl_inc s0 bom > 0)%Z.

Lemma sigma_ctrl_strct_pos :
forall s0 s1 : Site,
In_queue Message (inc_dec s0) (bom s1 owner) -> (sigma_ctrl s0 bom > 0)%Z.