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.