Definition maxF (f : Z -> perm_kind -> option permission) :=
    fun ofs k => match k with
              | Max => Some Freeable
              | Cur => f ofs k
              end.Definition allF (f : Z -> perm_kind -> option permission) :=
    fun (_ : Z) (_ : perm_kind) => Some Freeable.Fixpoint PList (f : (Z -> perm_kind -> option permission) ->
                      Z -> perm_kind -> option permission)
           l m : list (positive * (Z -> perm_kind -> option permission)) :=
    match l with
      | nil => nil
      | x :: l =>
        (Pos.of_nat x, f (PMap.get (Pos.of_nat x) m)) :: (PList f l m)
  end.

Lemma PList_app : forall l m x f, (PList f l m) ++ ((Pos.of_nat x, f (PMap.get (Pos.of_nat x) m)) :: nil) = PList f (l ++ (x :: nil)) m.