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).
Theorem LSB_comp : forall (x y : float) (n : nat), ~ is_Fzero x -> x = y :>R -> LSB x = LSB y.
Theorem maxDiv_opp : forall (v : Z) (p : nat), maxDiv v p = maxDiv (- v) p.
Theorem LSB_opp : forall x : float, LSB x = LSB (Fopp x).
Theorem maxDiv_abs : forall (v : Z) (p : nat), maxDiv v p = maxDiv (Zabs v) p.
Theorem LSB_abs : forall x : float, LSB x = LSB (Fabs x).