intuition.
unfold ratDistance, maxRat, minRat.
case_eq (bleRat r1 r2); case_eq (bleRat r2 r1); intuition.
apply ratSubtract_eqRat_compat;
eapply leRat_antisymm; eauto.
apply bleRat_total in H.
apply bleRat_total in H0.
apply ratSubtract_eqRat_compat;
eapply leRat_antisymm; eauto.
Qed.

Theorem ratMult_distrib_r : forall r1 r2 r3,
ratMult (ratAdd r2 r3) r1  == ratAdd (ratMult r2 r1) (ratMult r3 r1).