proposition: Lemma fold_identity : forall s, fold add s empty [=] s.
proof: Proof. intros. apply fold_rec with (P:=fun s acc => acc[=]s); auto with set. intros. rewrite H2; rewrite Add_Equal in H1; auto with set. Qed.
imports: MSetInterface PeanoNat DecidableTypeEx OrdersLists MSetFacts MSetDecide