unfold FPred in |- *; simpl in |- *.
generalize (Z_eq_bool_correct (nNormMin radix precision) (- pPred (vNum b)));
case (Z_eq_bool (nNormMin radix precision) (- pPred (vNum b)));
auto.
intros H'0; absurd (0 < pPred (vNum b))%Z; auto with zarith arith.
rewrite <- (Zopp_involutive (pPred (vNum b))); rewrite <- H'0.
apply Zle_not_lt; replace 0%Z with (- (0))%Z;
[ apply Zle_Zopp | simpl in |- *; auto ].
apply Zlt_le_weak; apply nNormPos; auto with float zarith.
unfold pPred in |- *; apply Zlt_succ_pred; simpl in |- *;
auto with float zarith.
simpl in |- *; apply vNumbMoreThanOne with (3 := pGivesBound); auto.
intros H';
generalize
(Z_eq_bool_correct (nNormMin radix precision) (nNormMin radix precision));
case (Z_eq_bool (nNormMin radix precision) (nNormMin radix precision)).
intros H'0; generalize (Z_eq_bool_correct (- dExp b) (- dExp b));
case (Z_eq_bool (- dExp b) (- dExp b)); auto.
intros H'1; Contradict H'1; auto.
intros H'1; Contradict H'1; auto.
Qed.

(* Specifications: *)
Theorem FPredSimpl4 :
forall x : float,
Fnum x <> (- pPred (vNum b))%Z ->
Fnum x <> nNormMin radix precision ->
FPred x = Float (Zpred (Fnum x)) (Fexp x).