intros x y H' H'0; unfold MSB in |- *.
rewrite <- H'0.
cut (Fdigit radix x <= Fdigit radix y)%Z;
[ unfold Zpred in |- *; auto with zarith | idtac ].
unfold Fdigit in |- *; apply inj_le.
apply digit_monotone; auto.
apply le_IZR.
apply Rmult_le_reg_l with (r := powerRZ radix (Fexp x));
auto with real zarith.
repeat rewrite (Rmult_comm (powerRZ radix (Fexp x))); auto.
pattern (Fexp x) at 2 in |- *; rewrite H'0; auto.
Qed.

Theorem MSB_monotone :
forall x y : float,
~ is_Fzero x -> ~ is_Fzero y -> (Fabs x <= Fabs y)%R -> (MSB x <= MSB y)%Z.