Definition dt_non_empty_r_def_0 (n : nat) : Prop :=
  forall (d : preDTA) (a : ad),
  MapGet bool (power (Map bool) (dta_app_ne d) (map_mini state d) n) a =
  Some true -> exists t : term, reconnaissance d a t.

Lemma dt_non_empty_fix_2 : forall (d : preDTA) (a : ad), MapGet bool (dta_non_empty_states d) a = Some true -> exists n : nat, MapGet bool (power (Map bool) (dta_app_ne d) (map_mini state d) n) a = Some true.