intros x H'; apply Rle_trans with (FtoRradix (Float 1%nat (MSB x))).
apply (oneExp_le radix); auto.
apply LSB_le_MSB; auto.
apply MSB_le_abs; auto.
Qed.

Theorem MSB_monotoneAux :
forall x y : float,
(Fabs x <= Fabs y)%R -> Fexp x = Fexp y -> (MSB x <= MSB y)%Z.