(** [split] derives two lists from a list of pairs *)

    Fixpoint split (l:list (A*B)) : list A * list B :=
      match l with
      | [] => ([], [])
      | (x,y) :: tl => let (left,right) := split tl in (x::left, y::right)
      end.

Lemma length_fst_split : forall (l:list (A*B)), length (fst (split l)) = length l.