intuition.
unfold ratSubtract.
rattac.
inversion l; clear l; subst.
omega.
rewrite H0.
unfold posnatToNat in *.
omega.
Qed.

Lemma ratSubtract_partition_leRat : forall r3 r1 r2 d1 d2,
ratSubtract r1 r3 <= d1 ->
ratSubtract r3 r2 <= d2 ->
ratSubtract r1 r2 <= d1 + d2.