Definition st_compatible_compat_def (s0 : state) : Prop :=
  forall s1 : state, st_compatible s0 s1 -> mpl_compat s0 s1.

Lemma st_compatible_compat_2 : forall m : Map prec_list, st_compatible_compat_def m -> forall m0 : Map prec_list, st_compatible_compat_def m0 -> st_compatible_compat_def (M2 prec_list m m0).