(** [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_map : forall (f g : A -> bool) (l : list A), filter f l = filter g l <-> map f l = map g l.