induction z; simpl in *; intuition.
eapply negligible_exp_den.
eapply negligible_eq.
eapply negligible_mult_ident.
eauto.
intuition.
rewrite <- ratMult_num_den.
eapply eqRat_terms; trivial.
unfold posnatToNat, natToPosnat, posnatMult.
eapply mult_1_l.
Qed.

Theorem negligible_const_num :
forall k,
negligible (fun n => k / expnat 2 n)%rat.