intuition.
rewrite <- (ratSubtract_ratAdd_inverse r2).
rewrite ratSubtract_ratAdd_assoc.
eapply ratAdd_leRat_compat; eauto.
intuition.
trivial.
Qed.

Lemma ratDistance_le_sum : forall r1 r2 d,
ratDistance r1 r2 <= d ->
r1 <= r2 + d.