intuition.
destruct (eq_Rat_dec r3 0).
repeat rewrite e.
repeat rewrite ratMult_0_r.
rewrite <- ratIdentityIndiscernables.
intuition.
unfold ratDistance, maxRat, minRat.
case_eq (bleRat r1 r2); intuition.
assert (bleRat (r1 * r3) ( r2 * r3) = true).
eapply ratMult_leRat_compat;
intuition.
rewrite H0.
rewrite ratMult_ratSubtract_distrib_r.
intuition.
case_eq (bleRat (r1 * r3) (r2 * r3)); intuition.
eapply leRat_ratMult_same_r in H0.
congruence.
intuition.
rewrite ratMult_ratSubtract_distrib_r.
intuition.
Qed.

Lemma ratMult_ratDistance_factor_l : forall r1 r2 r3,
ratDistance (r3 * r1) (r3 * r2) == r3 * (ratDistance r1 r2).