intuition.
eapply (modNat_add_same_l x y z).
rewrite plus_comm.
rewrite H.
rewrite plus_comm.
trivial.
Qed.

(* Specifications: *)
Lemma expnat_base_S : forall n k,
((expnat k n) + n * (expnat k (pred n)) <= expnat (S k) n)%nat.