intuition.
unfold ratDistance, maxRat, minRat.
case_eq (bleRat r1 r2); intuition;
apply ratSubtract_le; eauto.
Qed.

Lemma ratSubtract_eqRat_compat : forall r1 r2 r3 r4,
r1 == r3 ->
r2 == r4 ->
ratSubtract r1 r2 == ratSubtract r3 r4.