intuition.
eapply leRat_trans.
eapply (ratTriangleInequality _ _ (r3 + r2)).
eapply ratAdd_leRat_compat.
eapply eqRat_impl_leRat.
eapply ratDistance_add_same_r.
eapply eqRat_impl_leRat.
eapply ratDistance_add_same_l.
Qed.

(* Specifications: *)
Theorem ratMult_distrib : forall r1 r2 r3,
r1 * (r2 + r3) == r1 * r2 + r1 * r3.