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')).