intros x.
generalize (Z_eq_bool_correct (Fnum x) (- pPred (vNum b)));
case (Z_eq_bool (Fnum x) (- pPred (vNum b))); intros H'1.
rewrite FPredSimpl1; auto; rewrite FSuccSimpl1; auto.
unfold Fopp in |- *; simpl in |- *; rewrite H'1; auto with zarith.
generalize (Z_eq_bool_correct (Fnum x) (nNormMin radix precision));
case (Z_eq_bool (Fnum x) (nNormMin radix precision));
intros H'2.
generalize (Z_eq_bool_correct (Fexp x) (- dExp b));
case (Z_eq_bool (Fexp x) (- dExp b)); intros H'3.
replace x with (Float (Fnum x) (Fexp x)).
rewrite H'2; rewrite H'3; rewrite FPredSimpl3; unfold Fopp in |- *;
simpl in |- *; rewrite FSuccSimpl3; simpl in |- *;
auto.
rewrite <- Zopp_Zpred_Zs; rewrite Zopp_involutive; auto.
case x; simpl in |- *; auto.
rewrite FPredSimpl2; auto; rewrite FSuccSimpl2; unfold Fopp in |- *;
simpl in |- *; try rewrite Zopp_involutive;
auto.
rewrite H'2; auto.
rewrite FPredSimpl4; auto; rewrite FSuccSimpl4; auto.
unfold Fopp in |- *; simpl in |- *; rewrite <- Zopp_Zpred_Zs;
rewrite Zopp_involutive; auto.
unfold Fopp in |- *; simpl in |- *; Contradict H'1; rewrite <- H'1;
rewrite Zopp_involutive; auto.
unfold Fopp in |- *; simpl in |- *; Contradict H'2; auto with zarith.
Qed.

Theorem FPredDiff1 :
forall x : float,
Fnum x <> nNormMin radix precision ->
Fminus radix x (FPred x) = Float 1%nat (Fexp x) :>R.