proposition: Lemma null_diff : forall T, forall eq : Deq T, forall l1 l2 : list T, null (diff eq l1 l2) <=> forall x, LIn x l2 -> LIn x l1.
proof: Proof. induction l1; simpl; sp. trw IHl1; sp; split; sp. assert ({a = x} + {a <> x}) by auto; sp. right; apply_hyp. trw in_remove; sp. alltrewrite in_remove; sp. apply_in_hyp p; sp; subst; sp. Qed.
imports: UsefulTypes bin_rels Omega