Remark sigma_ctrl_copy_init :
 forall s0 : Site, sigma_ctrl_copy s0 bag_init = 0%Z.Remark sigma_ctrl_dec_init :
 forall s0 : Site, sigma_ctrl_dec s0 bag_init = 0%Z.Remark sigma_ctrl_inc_init :
 forall s0 : Site, sigma_ctrl_inc s0 bag_init = 0%Z.

Lemma sigma_ctrl_init : forall s0 : Site, sigma_ctrl s0 bag_init = 0%Z.