(* terme t reconnu en l'etat s : f^(high t)=true *)
Definition dt_non_empty_def_0 (d : preDTA) (a : ad)
(t : term) (pr : reconnaissance d a t) :=
forall n : nat,
term_high t <= n ->
MapGet bool (power (Map bool) (dta_app_ne d) (map_mini state d) n) a =
Some true.
Definition dt_non_empty_def_1 (d : preDTA) (s : state)
(t : term) (pr : state_reconnait d s t) :=
forall n : nat,
term_high t <= S n ->
st_non_empty (power (Map bool) (dta_app_ne d) (map_mini state d) n) s =
true.
Definition dt_non_empty_def_2 (d : preDTA) (p : prec_list)
(t : term_list) (pr : liste_reconnait d p t) :=
forall n : nat,
term_high_0 t <= n ->
pl_non_empty (power (Map bool) (dta_app_ne d) (map_mini state d) n) p =
true.

Lemma dt_non_empty_0 :
forall (d : preDTA) (a : ad) (t : term) (ladj : state)
(e : MapGet state d a = Some ladj) (s : state_reconnait d ladj t),
dt_non_empty_def_1 d ladj t s ->
dt_non_empty_def_0 d a t (rec_dta d a t ladj e s).