intuition.
unfold ratSubtract.
rattac.
arithNormalize.
rewrite (plus_comm (n2 * x0 * x1 * x0 * x1 * x)).
rewrite NPeano.Nat.sub_add_distr.
apply minus_eq_compat.
rewrite <- NPeano.Nat.add_sub_assoc.
rewrite minus_diag_eq.
rewrite plus_0_r.
do 5 arithSimplify.
do 5 arithSimplify.
eapply le_eq.
do 5 arithSimplify.
do 5 arithSimplify.
Qed.

(* Specifications: *)
Lemma ratSubtract_add_same_l : forall r1 r2 r3,
r1 <= r3 ->
ratSubtract (r2 + r3) (r2 + r1) == ratSubtract r3 r1.