(* 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')).