(** [partition] *)

    Fixpoint partition (l:list A) : list A * list A :=
      match l with
      | [] => ([], [])
      | x :: tl => let (g,d) := partition tl in
                   if f x then (x::g,d) else (g,x::d)
      end.

Lemma filter_ext : forall (f g : A -> bool), (forall a, f a = g a) -> forall l, filter f l = filter g l.