intuition.
unfold ratMult, ratSubtract.
rattac.
inversion H; clear H; subst.
arithNormalize.
f_equal.
do 6 arithSimplify.
do 6 arithSimplify.
Qed.

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