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.

(* Specifications: *)
Lemma mpl_compat_8_0 : mpl_compat_8_def (M0 prec_list).
Lemma mpl_compat_8_1 :
forall (a : ad) (a0 : prec_list), mpl_compat_8_def (M1 prec_list a a0).
Lemma mpl_compat_8_2 :
forall m : state,
mpl_compat_8_def m ->
forall m0 : state,
mpl_compat_8_def m0 -> mpl_compat_8_def (M2 prec_list m m0).
Lemma mpl_compat_8_3 : forall m : state, mpl_compat_8_def m.
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.