intros v p; elim p; simpl in |- *; auto.
intros n H; case (ZdividesP v (radix * Zpower_nat radix n));
case (ZdividesP (- v) (radix * Zpower_nat radix n)); auto.
intros Z1 Z2; case Z1.
case Z2; intros z1 Hz1; exists (- z1)%Z; rewrite Hz1; ring.
intros Z1 Z2; case Z2.
case Z1; intros z1 Hz1; exists (- z1)%Z.
rewrite <- (Zopp_involutive v); rewrite Hz1; ring.
Qed.

Theorem LSB_opp : forall x : float, LSB x = LSB (Fopp x).
intros x; unfold LSB in |- *; simpl in |- *.