intros H'; case H'; auto.
intros n H' H'0; inversion_clear H'0.
rewrite H; generalize H; case q; simpl in |- *; auto with arith; intros;
discriminate.
Qed.

(* Specifications: *)
Lemma divides_antisym : forall a b : nat, divides a b -> divides b a -> a = b.
Lemma not_lt_div : forall a b : nat, 0 < b -> b < a -> ~ divides a b.
intros a b H'1 H'2; red in |- *; intros H'3; absurd (a <= b); auto with arith.