intros v p; elim p; simpl in |- *; auto.
intros n H; case (ZdividesP v (radix * Zpower_nat radix n));
case (ZdividesP (Zabs v) (radix  * Zpower_nat radix n));
auto.
intros Z1 Z2; case Z1.
case Z2; intros z1 Hz1; exists (Zabs z1); rewrite Hz1.
rewrite Zabs_Zmult; f_equal. apply Zabs_eq. auto with zarith.
intros Z1 Z2; case Z2.
case Z1; intros z1 Hz1.
case (Zle_or_lt v 0); intros Z4.
exists (- z1)%Z; rewrite <- (Zopp_involutive v);
rewrite <- (Zabs_eq_opp v); auto; rewrite Hz1; ring.
exists z1; rewrite <- (Zabs_eq v); auto with zarith; rewrite Hz1; ring.
Qed.

(* Specifications: *)
Theorem LSB_abs : forall x : float, LSB x = LSB (Fabs x).
intros x; unfold LSB in |- *; simpl in |- *.