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 kill_empty_correct_wrt_sign_invar_0 : forall (p p' : prec_list) (m : Map bool) (n : nat), pl_tl_length p n -> prec_list_kill m p = Some p' -> pl_tl_length p' n.