intuition.
eapply negligible_eq.
eapply (@negligible_const_mult k (pos 1)).
eapply negligible_exp_den.
intuition.
rewrite <- ratMult_num_den.
eapply eqRat_terms.
eapply mult_1_r.
unfold natToPosnat, posnatToNat, posnatMult.
eapply mult_1_l.
Qed.

Theorem negligible_poly_num :
forall f,
polynomial f ->
negligible (fun n => f n / expnat 2 n)%rat.