(** [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 in_split_l : forall (l:list (A*B))(p:A*B), In p l -> In (fst p) (fst (split l)).