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.
Lemma dt_non_empty_fix : forall (d : preDTA) (a : ad), MapGet bool (dta_non_empty_states d) a = Some true <-> (exists t : term, reconnaissance d a t).
Lemma dt_non_empty_lazy_fix : forall (d : preDTA) (a : ad), MapGet bool (dta_non_empty_states_lazy d) a = Some true <-> (exists t : term, reconnaissance d a t).