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.