rewrite Rmult_1_l.
rewrite <- Zpower_nat_Z_powerRZ; auto with real zarith.
rewrite INR_IZR_INZ; auto with real zarith.
apply Rle_lt_trans with (Zabs n); [rewrite (Zabs_eq (Z_of_nat n))|idtac];auto with real zarith.
Qed.

Theorem boundBoundNat : forall n : nat, Fbounded b (boundNat n).
intros n; repeat split; unfold boundNat in |- *; simpl in |- *;
auto with zarith.