intuition.
unfold ratSubtract.
rattac.
arithNormalize.
rewrite <- (mult_assoc (n1 * x)).
rewrite (mult_comm x x0).
rewrite mult_assoc.
remember (n1 * x * x0 * x)%nat as a.
repeat rewrite <- (mult_assoc n0).
rewrite (mult_comm x).
omega.
Qed.

Lemma ratSubtract_ratAdd_inverse_2 : forall r1 r2,
r2 <= r1 ->
r2 + ratSubtract r1 r2 == r1.