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_kill_empty : forall (d : preDTA) (a : ad) (sigma : signature), predta_correct_wrt_sign d sigma -> ((exists s : state, MapGet state (preDTA_kill (dta_non_empty_states d) d) a = Some s) <-> (exists t : term, reconnaissance d a t)).