intros b z H; split; auto.
change (Zabs (Zpred (Zpos (vNum b))) < Zpos (vNum b))%Z in |- *.
rewrite Zabs_eq; auto with zarith.
Qed.

Theorem maxMax :
forall (b : Fbound) (p : float) (z : Z),
Fbounded b p ->
(Fexp p <= z)%Z -> (Fabs p < Float (Zpos (vNum b)) z)%R.