intuition.
unfold negligible in *.
intuition.
edestruct H.
econstructor.
intuition.
eapply H1.
eauto.
rewrite H3.
rewrite <- H0.
intuition.
Qed.

Lemma negligible_le :
forall f1 f2,
(forall n, f2 n <= f1 n)%rat ->
negligible f1 ->
negligible f2.