proposition: Lemma equiv_add_rem : forall (a:A) (P Q:set), ~ Q a -> equiv (add a Q) P -> equiv Q (rem a P).
proof: Proof. intros; assert (incl (add a Q) P); auto. assert (incl P (add a Q)); auto. case (incl_rem_add_iff a P Q); auto. Qed.
imports: Coq(Arith) Coq(Lt)