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_0 : forall (d : preDTA) (p p' : prec_list), prec_list_kill (dta_non_empty_states d) p = Some p' -> exists plp : pl_path, pl_path_incl plp p'.