Definition mpl_compat_8_def (s : state) : Prop :=
  forall (a c : ad) (pl l : prec_list),
  MapGet prec_list s c = Some l ->
  a <> c -> MapGet prec_list (union_mpl_0 a pl s) c = Some l.

Lemma mpl_compat_8_1 : forall (a : ad) (a0 : prec_list), mpl_compat_8_def (M1 prec_list a a0).