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_1 : forall (s : state) (sigma : signature) (m : Map bool), state_correct_wrt_sign s sigma -> state_correct_wrt_sign (states_kill_aux m s) sigma.