intros x H'.
case (Req_dec x r); intros H'1.
exists x.
rewrite <- H'1.
red in |- *; split; [ case H' | split ]; auto with real.
(* A maximum always exists *)
exists (FNSucc b radix precision x).
apply MinMax; auto.
Qed.

(* Specifications: *)
Theorem MinBinade :
forall (r : R) (p : float),
Fbounded b p ->
(p <= r)%R -> (r < FNSucc b radix precision p)%R -> isMin r p.