intros x y H' H'0 H'1 H'2.
cut (y <= 2%nat * x)%R; [ intros Le1 | idtac ].
case (Rle_or_lt x y); intros Le2; auto.
apply oppBoundedInv; auto.
rewrite Fopp_Fminus.
apply SterbenzAux; auto with real.
apply SterbenzAux; auto with real.
apply Rmult_le_reg_l with (r := (/ 2%nat)%R).
apply Rinv_0_lt_compat; auto with real.
rewrite <- Rmult_assoc; rewrite Rinv_l; auto with real.
rewrite Rmult_1_l; auto.
Qed.

(* Specifications: *)
Theorem BminusSameExpAux :
forall x y : float,
Fbounded b x ->
Fbounded b y ->
(0 <= y)%R -> (y <= x)%R -> Fexp x = Fexp y -> Fbounded b (Fminus radix x y).