(** [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_cons1 a l l1 l2: partition l = (l1, l2) -> f a = true -> partition (a::l) = (a::l1, l2).