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 :
forall (s : state) (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.