proposition: Lemma rdec_trans_sigma_ctrl : sigma_ctrl s0 (bm (rec_dec_trans c0 s1 s2)) = (if eq_site_dec s0 s2 then (sigma_ctrl s0 (bm c0) - 1)%Z else sigma_ctrl s0 (bm c0)).
proof: Proof. intros; unfold sigma_ctrl in |- *. rewrite rdec_trans_sigma_copy. rewrite rdec_trans_sigma_dec. rewrite rdec_trans_sigma_inc. case (eq_site_dec s0 s2); intro. omega. trivial. Qed.
imports: init table_act mess_act