Definition dta_ref_ok_check (d : DTA) : bool :=
  match d with
  | dta p a => predta_ref_ok_check p
  end.

(* Specifications: *)
Lemma dta_ref_ok_check_correct : forall d : DTA, DTA_ref_ok d -> dta_ref_ok_check d = true.
Lemma dta_ref_ok_check_complete : forall d : DTA, dta_ref_ok_check d = true -> DTA_ref_ok d.