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 oppBoundedInv : forall (b : Fbound) (x : float), Fbounded b (Fopp x) -> Fbounded b x.