(** [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.

Theorem partition_length l l1 l2: partition l = (l1, l2) -> length l = length l1 + length l2.