intros p; unfold FSucc, Fodd, Feven in |- *.
generalize (Z_eq_bool_correct (Fnum p) (pPred (vNum b)));
case (Z_eq_bool (Fnum p) (pPred (vNum b))); intros H'1.
rewrite H'1; simpl in |- *; auto.
unfold pPred in |- *; rewrite pGivesBound; unfold nNormMin in |- *.
case (OddEvenDec radix); auto with zarith.
intros H'; split; intros H'0; auto with zarith.
apply EvenMultInv with (n := radix); auto.
pattern radix at 1 in |- *; rewrite <- Zpower_nat_1;
rewrite <- Zpower_nat_is_exp.
replace (1 + pred precision) with precision;
[ idtac | inversion precisionGreaterThanOne; auto ].
rewrite (Zsucc_pred (Zpower_nat radix precision)); auto with zarith.
intros H'; split; intros H'0; auto with zarith.
replace (pred precision) with (S (pred (pred precision))); auto with zarith.
Contradict H'0; apply OddNEven.
replace (Zpred (Zpower_nat radix precision)) with
(Zpower_nat radix precision + - (1))%Z;
[ idtac | unfold Zpred in |- *; simpl in |- *; auto ].
replace precision with (S (pred precision));
[ auto with zarith | inversion precisionGreaterThanOne; auto ].
generalize (Z_eq_bool_correct (Fnum p) (- nNormMin radix precision));
case (Z_eq_bool (Fnum p) (- nNormMin radix precision));
intros H'2.
generalize (Z_eq_bool_correct (Fexp p) (- dExp b));
case (Z_eq_bool (Fexp p) (- dExp b)); intros H'3.
simpl in |- *; auto with zarith.
simpl in |- *; auto with zarith.
rewrite H'2; unfold pPred, nNormMin in |- *; rewrite pGivesBound.
case (OddEvenDec radix); auto with zarith.
intros H'; split; intros H'0; auto with zarith.
apply EvenOpp; apply OddSEvenInv; rewrite <- Zsucc_pred; auto with zarith.
Contradict H'0; replace precision with (S (pred precision));
[ auto with zarith | inversion precisionGreaterThanOne; auto ].
intros H'; split; intros H'0; auto with zarith.
Contradict H'0; replace (pred precision) with (S (pred (pred precision)));
[ auto with zarith | auto with zarith ].
replace precision with (S (pred precision));
[ auto with zarith | inversion precisionGreaterThanOne; auto ].
apply OddOpp; apply EvenSOddInv; rewrite <- Zsucc_pred; auto with zarith.
simpl in |- *; auto with zarith.
Qed.

(* Specifications: *)
Theorem FoddSuc :
forall p : float, Fodd p -> Feven (FSucc b radix precision p).