Section F2.
Variable b : Fbound.
Variable precision : nat.
Let radix := 2%Z.
Let FtoRradix := FtoR radix.
Local Coercion FtoRradix : float >-> R.
unfold radix in |- *; red in |- *; simpl in |- *; auto.
Qed.
Hint Resolve TwoMoreThanOne.
Hypothesis precisionNotZero : 1 < precision.
Hypothesis pGivesBound : Zpos (vNum b) = Zpower_nat radix precision.
unfold nNormMin in |- *.
generalize precisionNotZero; case precision.
intros H'2; Contradict H'2; auto with zarith.
intros n; case n.
intros H'2; Contradict H'2; auto with zarith.
intros n0 H'2; replace (pred (S (S n0))) with (S n0).
apply EvenExp; auto.
exists 1%Z; ring.
simpl in |- *; auto.
Qed.

Theorem EvenFNSuccFNSuccMid :
forall p : float,
Fbounded b p ->
FNeven b radix precision p ->
Fminus radix (FNSucc b radix precision (FNSucc b radix precision p))
(FNSucc b radix precision p) = Fminus radix (FNSucc b radix precision p) p
:>R.