intros.
apply Trans with (seq_set (empty_seq A)); auto with algebra.
simpl in |- *.
red in |- *.
split.
intro.
simpl in H.
inversion H; (apply False_ind; auto with algebra).
intro.
simpl in H.
contradiction.
Qed.
Hint Resolve seq_set_empty_seq_is_empty: algebra.

(* The only sequence of empty-set-elements is the empty sequence *)
Lemma no_seq_n_empty :
forall (n : Nat) (A : Setoid) (W : part_set A),
W =' empty A in _ -> seq n W -> n =' 0 in _.