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 eqExpMax : forall (b : Fbound) (p q : float), Fbounded b p -> Fbounded b q -> (Fabs p <= q)%R -> exists r : float, Fbounded b r /\ r = p :>R /\ (Fexp r <= Fexp q)%Z.