rattac.
arithNormalize.
assert (n * x * x0 <= n0 * x0 * x1)%nat.
rewrite (mult_comm (n0 * x0) x1).
rewrite mult_assoc.
apply mult_le_compat; trivial.
rewrite (mult_comm x1).
trivial.
rewrite <- plus_0_r at 1.
apply plus_le_compat; eauto.
apply le_0_n.
Qed.

Lemma ratAdd_any_leRat_r : forall r1 r2 r3,
r1 <= r2 ->
r1 <= r3 + r2.