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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
(* correction d'un preDTA : pas de référence à des adresses extérieures à l'automate *)
Definition prec_list_ref_ok (p : prec_list) (d : preDTA) : Prop :=
forall a : ad,
prec_occur p a -> exists s : state, MapGet state d a = Some s.
Definition state_ref_ok (s : state) (d : preDTA) : Prop :=
forall (a : ad) (p : prec_list),
MapGet prec_list s a = Some p -> prec_list_ref_ok p d.
Definition preDTA_ref_ok (d : preDTA) : Prop :=
forall (a : ad) (s : state) (c : ad) (pl : prec_list) (b : ad),
MapGet state d a = Some s ->
MapGet prec_list s c = Some pl ->
prec_occur pl b -> exists s0 : state, MapGet state d b = Some s0.
Definition preDTA_ref_ok_distinct (d d' : preDTA) : Prop :=
forall (a : ad) (s : state),
MapGet state d a = Some s -> state_ref_ok s d'.
Definition DTA_ref_ok (d : DTA) : Prop :=
match d with
| dta p a => preDTA_ref_ok p
end.

Lemma prec_list_ref_ok_destr :
forall (a : ad) (la ls : prec_list) (d : preDTA),
prec_list_ref_ok (prec_cons a la ls) d ->
prec_list_ref_ok la d /\ prec_list_ref_ok ls d.