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 dta_kill_empty_states_lazy_semantics : forall (d : DTA) (t : term), reconnait d t <-> reconnait (DTA_kill_empty_states_lazy d) t.