Fixpoint containsList_upto_n (n m:nat): n <= m -> seq.seq (sigT (fun i => i < m)):=
      match n with
      | O => fun _ => nil
      | S n' => fun (H: S n' <= m) =>
                 (existT (fun i => i < m) (m-(S n')) (lt_sub H)) ::
                 (containsList_upto_n n' m) (leq_stepdown H)                                  
      end.

Lemma leq_refl: forall n, n <= n.