(* ls1 is the smaller set.  This function returns a permutation of ls2 where the first elements of ls2 match the order of the elements in ls1.  This function only works if ls1 is a subset of ls2. *)
Fixpoint matchOrder (A : Set)(eqd : eq_dec A)(ls1 ls2 : list A) :=
  match ls1 with
    | nil => ls2
    | a :: ls1' => 
      a :: (matchOrder eqd ls1' (removeFirst eqd ls2 a))
  end.

Lemma matchOrder_not_in : forall (A : Set)(eqd : eq_dec A)(ls1 ls2 : list A) a, (forall a, In a ls1 -> In a ls2) -> ~In a ls2 -> ~In a (matchOrder eqd ls1 ls2).