intros P H' f1 f2 H'0 HZ.
apply (oneExp_Zlt radix); auto.
apply Rlt_le_trans with (Fulp b radix precision f2).
apply Rle_lt_trans with (FtoRradix (Fabs (Fminus radix f1 f2))).
unfold FtoRradix in |- *; apply MSB_le_abs; auto.
unfold FtoRradix in |- *; rewrite Fabs_correct; auto with arith;
rewrite Fminus_correct; auto with arith.
apply RoundedModeUlp with (4 := H'); auto.
apply FUlp_Le_LSigB; auto.
apply RoundedModeBounded with (1 := H') (2 := H'0); auto.
Qed.

(* Specifications: *)
Theorem LSBMinus :
forall p q : float,
~ is_Fzero (Fminus radix p q) ->
(Zmin (LSB radix p) (LSB radix q) <= LSB radix (Fminus radix p q))%Z.