(** [combine] is the opposite of [split].
      Lists given to [combine] are meant to be of same length.
      If not, [combine] stops on the shorter list *)

    Fixpoint combine (l : list A) (l' : list B) : list (A*B) :=
      match l,l' with
      | x::tl, y::tl' => (x,y)::(combine tl tl')
      | _, _ => []
      end.

Lemma split_combine : forall (l: list (A*B)), forall l1 l2, split l = (l1, l2) -> combine l1 l2 = l.