intuition.
unfold ratDistance, maxRat, minRat.
case_eq (bleRat r 0); intuition.
rewrite ratSubtract_0;
eapply rat0_le_all.
apply bleRat_total in H0.
rewrite ratSubtract_0_r.
trivial.
Qed.

Lemma ratSubtract_0_inv : forall r1 r2,
ratSubtract r1 r2 == 0 ->
r1 <= r2.