intuition.
unfold ratSubtract.
rattac.
arithNormalize.
rewrite  minus_plus_assoc.
f_equal.
f_equal.
do 5 arithSimplify.
do 5 arithSimplify.
do 3 (eapply mult_le_compat; trivial).
repeat rewrite <- mult_assoc.
repeat rewrite (mult_comm x).
repeat rewrite mult_assoc.
apply mult_le_compat; trivial.
Qed.

Lemma ratAdd_add_same_r : forall r1 r2 r3,
r1 + r2 == r3 + r2 ->
r1 == r3.