proposition: Lemma copy_trans_sigma_ctrl : sigma_ctrl s0 (bm (copy_trans c0 s1 s2)) = (if eq_site_dec s0 s1 then (sigma_ctrl s0 (bm c0) + 1)%Z else sigma_ctrl s0 (bm c0)).
proof: Proof. intros; unfold sigma_ctrl in |- *. rewrite copy_trans_sigma_copy. rewrite copy_trans_sigma_dec. rewrite copy_trans_sigma_inc. case (eq_site_dec s0 s1); intro. omega. trivial. Qed.
imports: init table_act mess_act