unfold negligible in *.
intuition.
destruct (H (S c)).
exists x.
intuition.
eapply H0.
omega.
simpl.
assert ( (RatIntro 1 (natToPosnat (expnat_nz (S c) pf_nz)))  ==
RatIntro 1 (posnatMult (pos x0) (pos expnat x0 c)) )%rat.
eapply eqRat_terms; trivial.
simpl in *.
rewrite H3.
rewrite ratMult_denom.
rewrite H2.
rewrite <- ratMult_assoc.
rewrite <- ratMult_num_den.
rewrite num_dem_same_rat1.
rewrite ratMult_1_l.
intuition.
unfold natToPosnat, posnatToNat, posnatMult.
omega.
Qed.

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