intuition.
unfold maxRat.
case_eq (bleRat r1 r2); intuition.
case_eq (bleRat r2 r1); intuition.
eapply leRat_impl_eqRat; trivial.
apply bleRat_total in H.
rewrite H.
intuition.
Qed.

Lemma ratDistance_le_max_triv : forall r1 r2,
ratDistance r1 r2 <= maxRat r1 r2.