(* What it is to be a maximum *)
 
Definition isMax (r : R) (max : float) :=
  Fbounded b max /\
  (r <= max)%R /\
  (forall f : float, Fbounded b f -> (r <= f)%R -> (max <= f)%R).

Theorem FmaxRep : forall p q : float, isMax p q -> exists m : Z, q = Float m (Fexp p) :>R.