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.