intuition.
eapply ratAdd_add_same_r.
eapply eqRat_trans.
apply ratAdd_comm.
rewrite H.
apply ratAdd_comm.
Qed.

Lemma ratDistance_add_same_r : forall r1 r2 r3,
(ratDistance (r1 + r2) (r3 + r2)) == (ratDistance r1 r3).