intuition.
apply (@ratSubtract_leRat_l (r2 + r1) (r3 + r1) r1) in H.
rewrite <- (@ratSubtract_ratAdd_inverse r1 r2).
rewrite ratAdd_comm.
rewrite H.
rewrite ratAdd_comm.
rewrite ratSubtract_ratAdd_inverse.
intuition.
Qed.

Lemma leRat_ratMult_same_r : forall r1 r2 r3,
(~r1 == 0) ->
r2 * r1 <= r3 * r1 ->
r2 <= r3.