Remark rcop3_trans_sigma_copy :
 sigma_ctrl_copy s0 (bm (rec_copy3_trans c0 s1 s2)) =
 (if eq_site_dec s0 s1
  then  (sigma_ctrl_copy s0 (bm c0) - 1)%Z
  else  sigma_ctrl_copy s0 (bm c0)).Remark rcop3_trans_sigma_dec :
 sigma_ctrl_dec s0 (bm (rec_copy3_trans c0 s1 s2)) =
 sigma_ctrl_dec s0 (bm c0).Remark rcop3_trans_sigma_inc :
 sigma_ctrl_inc s0 (bm (rec_copy3_trans c0 s1 s2)) =
 (if eq_site_dec s0 s1
  then  (sigma_ctrl_inc s0 (bm c0) + 1)%Z
  else  sigma_ctrl_inc s0 (bm c0)).

(* Specifications: *)
Lemma rcop3_trans_sigma_ctrl : sigma_ctrl s0 (bm (rec_copy3_trans c0 s1 s2)) = sigma_ctrl s0 (bm c0).