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 :
forall (d : preDTA) (a : ad) (t : term),
reconnaissance (preDTA_kill (dta_non_empty_states d) d) a t ->
reconnaissance d a t.