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_2 : forall (d : preDTA) (p : prec_list) (plp : pl_path), pl_path_incl plp p -> pl_path_true plp (dta_non_empty_states d) -> exists tl : term_list, pl_path_recon d tl plp.