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