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.

(* Specifications: *)
Lemma dt_non_empty_r_3 : dt_non_empty_r_def_0 0.
Lemma dt_non_empty_r_4 :
forall (p : prec_list) (n : nat) (d : preDTA) (pl : pl_path),
dt_non_empty_r_def_0 n ->
pl_path_true pl (power (Map bool) (dta_app_ne d) (map_mini state d) n) ->
pl_path_incl pl p -> exists tl : term_list, liste_reconnait d p tl.
Lemma dt_non_empty_r_5 :
forall n : nat, dt_non_empty_r_def_0 n -> dt_non_empty_r_def_0 (S n).
Lemma dt_non_empty_r :
forall (n : nat) (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_0 :
forall d : preDTA,
lower_fix_point bool (ensemble_base state d) lem (dta_app_ne d)
(dta_non_empty_states d).
Lemma dt_non_empty_fix_1 :
forall (d : preDTA) (a : ad) (n : nat),
MapGet bool (power (Map bool) (dta_app_ne d) (map_mini state d) n) a =
Some true -> MapGet bool (dta_non_empty_states d) a = Some true.
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.