intros x n H'; unfold LSB, Fdigit in |- *; simpl in |- *.
rewrite digitAdd; auto with arith.
rewrite maxDivPlus; auto.
rewrite inj_plus; ring.
Qed.

Theorem LSB_comp :
forall (x y : float) (n : nat), ~ is_Fzero x -> x = y :>R -> LSB x = LSB y.