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 FopRepAux : forall (b : Fbound) (z : Z) (p : R), ex (fun r : float => r = (- p)%R :>R /\ Fbounded b r /\ Fexp r = z) -> ex (fun r : float => r = p :>R /\ Fbounded b r /\ Fexp r = z).