(* A function that returns a list containing all the bounded smaller than a given real *)
 
Definition mBFloat (p : R) :=
  map (fun p : Z * Z => Float (fst p) (snd p))
    (mProd Z Z (Z * Z)
       (mZlist (- pPred (vNum b)) (pPred (vNum b)))
       (mZlist (- dExp b) (Fexp (boundR p)))).

Theorem mBFadic_correct3 : forall r : R, In (Fopp (boundR r)) (mBFloat r).