intros v n H.
replace (digit radix v + n) with (digit radix (v * Zpower_nat radix n)); auto.
apply sym_equal.
apply maxDivUniqueInverseDigit; auto.
red in |- *; intros Z1; case (Zmult_integral _ _ Z1); intros Z2.
case H; auto.
absurd (0 < Zpower_nat radix n)%Z; auto with zarith.
rewrite Zpower_nat_is_exp.
repeat rewrite (fun x : Z => Zmult_comm x (Zpower_nat radix n)).
apply ZdividesMult; auto.
case (maxDivUniqueDigit v); auto.
replace (S (maxDiv v (digit radix v) + n)) with
(S (maxDiv v (digit radix v)) + n); auto.
rewrite Zpower_nat_is_exp.
repeat rewrite (fun x : Z => Zmult_comm x (Zpower_nat radix n)).
red in |- *; intros H'.
absurd (Zdivides v (Zpower_nat radix (S (maxDiv v (digit radix v))))).
case (maxDivUniqueDigit v); auto.
apply ZdividesDiv with (p := Zpower_nat radix n); auto with zarith.
apply digitAdd; auto with zarith.
Qed.
Definition LSB (x : float) :=
(Z_of_nat (maxDiv (Fnum x) (Fdigit radix x)) + Fexp x)%Z.

(* Specifications: *)
Theorem LSB_shift :
forall (x : float) (n : nat), ~ is_Fzero x -> LSB x = LSB (Fshift radix n x).