proposition: Remark copy_trans_sigma_copy : sigma_ctrl_copy s0 (bm (copy_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)).
proof: Proof. intros; unfold sigma_ctrl_copy in |- *. case (eq_site_dec s0 s1); intro. apply sigma__S with (eq_E_dec := eq_site_dec) (x0 := s2). exact finite_site. rewrite copy_trans_ctrl_copy. rewrite e; rewrite case_eq; apply case_eq. intros; rewrite copy_trans_ctrl_copy. rewrite e; rewrite case_eq; apply case_ineq; trivial. apply sigma_simpl. intros; rewrite copy_trans_ctrl_copy. apply case_ineq; trivial. Qed.
imports: init table_act mess_act