unfold negligible in *.
intuition.
destruct (poly_lt_exp c).
exists x.
intuition.
eapply (rat_num_not_le).
eapply H1.
unfold posnatToNat, natToPosnat.
eapply H.
omega.
Qed.

Theorem negligible_const_mult :
forall (n : nat) d f,
negligible f ->
negligible (fun x => (RatIntro n d) * (f x))%rat.