Record Fbound : Set := Bound {vNum : positive; dExp : N}.Record Fbound : Set := Bound {vNum : positive; dExp : N}.Record Fbound : Set := Bound {vNum : positive; dExp : N}.Record Fbound : Set := Bound {vNum : positive; dExp : N}.Definition Fbounded (b : Fbound) (d : float) :=
  (Zabs (Fnum d) < Zpos (vNum b))%Z /\ (- dExp b <= Fexp d)%Z.

Theorem maxFbounded : forall (b : Fbound) (z : Z), (- dExp b <= z)%Z -> Fbounded b (Float (Zpred (Zpos (vNum b))) z).