Definition dt_kill_empty_def_1 (n : nat) : Prop :=
forall (d : preDTA) (a : ad) (t : term),
term_high t <= n ->
reconnaissance (preDTA_kill (dta_non_empty_states d) d) a t ->
reconnaissance d a t.

Lemma dt_kill_empty_r_1 :
forall (p' : prec_list) (n : nat) (d : preDTA) (p : prec_list)
(tl : term_list),
dt_kill_empty_def_1 n ->
term_high_0 tl <= n ->
liste_reconnait (preDTA_kill (dta_non_empty_states d) d) p tl ->
prec_list_kill (dta_non_empty_states d) p' = Some p ->
liste_reconnait d p' tl.