intros x y H' H'0; rewrite <- oneZplus.
replace (radix * Float 1%nat (MSB x + MSB y))%R with
(FtoRradix (Float 1%nat (Zsucc (MSB x + MSB y)))).
apply (oneExp_le radix); auto.
apply mult_le_MSBAux; auto.
unfold FtoRradix, FtoR in |- *; simpl in |- *.
rewrite powerRZ_Zs; auto with real zarith; ring.
Qed.

Theorem MSB_mix :
forall x y : float,
~ is_Fzero x ->
~ is_Fzero y ->
(Fabs x * Float 1%nat (MSB y) < radix * (Fabs y * Float 1%nat (MSB x)))%R.