proposition: Lemma incl_rem_add: forall (a:A) (P Q:set), (P a) -> incl Q (rem a P) -> incl (add a Q) P.
proof: Proof. unfold rem, add, incl; intros; auto. case H1; intro; subst; auto. case (H0 x); auto. Qed.
imports: Coq(Arith) Coq(Lt)