intros x.
rewrite (MSB_abs x).
unfold MSB, FtoRradix, FtoR in |- *.
rewrite <- Zsucc_pred; simpl in |- *.
rewrite powerRZ_add; auto with real zarith.
rewrite Rmult_1_l.
repeat rewrite (fun r : R => Rmult_comm r (powerRZ radix (Fexp x))).
apply Rmult_lt_compat_l; auto with real zarith.
rewrite <- Zpower_nat_Z_powerRZ; auto with arith.
apply Rlt_IZR.
unfold Fdigit in |- *; auto with arith.
unfold Fabs in |- *; simpl in |- *.
pattern (Zabs (Fnum x)) at 1 in |- *; rewrite <- (Zabs_eq (Zabs (Fnum x)));
auto with zarith.
Qed.

(* Specifications: *)
Theorem LSB_le_abs :
forall x : float, ~ is_Fzero x -> (Float 1%nat (LSB x) <= Fabs x)%R.