(* 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 isMax_inv1 : forall (p : float) (r : R), isMax r p -> (r <= p)%R.