intros f1 f2 H' H'0 H'1; Casec H'; intros tmp; Elimc tmp; intros H1 H2.
apply MSBisMin; auto.
rewrite (MSB_opp radix f1).
rewrite (MSB_opp radix f2).
apply MSBisMin; auto with float.
unfold FtoRradix in |- *; rewrite Fopp_correct.
replace 0%R with (-0)%R; auto with real.
unfold FtoRradix in |- *; rewrite Fopp_correct; auto with float.
Qed.

Theorem MSBBoundNotZero :
forall P : R -> float -> Prop,
RoundedModeP b radix P ->
forall f1 f2 : float,
P f1 f2 -> f1 <> 0%R :>R -> (- dExp b <= MSB radix f1)%Z -> f2 <> 0%R :>R.