intuition.
unfold ratSubtract, ratAdd.
rattac.
arithNormalize.
rewrite NPeano.Nat.sub_add_distr.
f_equal.
f_equal.
do 5 arithSimplify.
do 5 arithSimplify.
Qed.

Lemma ratSubtract_ratAdd_assoc_1 : forall r1 r2 r3,
r3 <= r2 ->
ratSubtract (r1 + r2) r3 == r1 + (ratSubtract r2 r3).