intuition.
unfold ratSubtract.
rattac.
arithNormalize.
rewrite NPeano.Nat.sub_add_distr.
apply minus_eq_compat.
rewrite plus_comm.
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.

Lemma minus_plus_assoc : forall n1 n2 n3,
(n3 <= n2 ->
(n1 + n2) - n3 = n1 + (n2 - n3))%nat.