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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   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
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(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 02110-1301 USA                                                     *)
(* conservation de l'invariant de compatibilité par rapport à une signature pour l'union *)
(* conservation de l'invariant ref_ok pour l'union *)

Lemma udta_conv_0_ref_ok_invar_0 :
forall (d : preDTA) (a : ad) (s : state) (c : ad) (p : prec_list) (b : ad),
MapGet state (udta_conv_0 d) (uad_conv_0 a) = Some s ->
MapGet prec_list s c = Some p ->
prec_occur p b ->
exists s' : state,
(exists p' : prec_list,
(exists b' : ad,
MapGet state d a = Some s' /\
MapGet prec_list s' c = Some p' /\
p = upl_conv_0 p' /\
s = umpl_conv_0 s' /\ b = uad_conv_0 b' /\ prec_occur p' b')).