intros x y H' H'0 H'1; rewrite FPredFopFSucc.
rewrite <- (Fopp_Fopp x).
unfold FtoRradix in |- *; rewrite Fopp_correct with (x := Fopp x).
rewrite Fopp_correct with (x := FSucc b radix precision (Fopp y));
auto with float real.
apply Ropp_le_contravar.
apply FSuccProp; auto with float.
repeat rewrite Fopp_correct; auto with real.
Qed.

Theorem FPredZleEq :
forall p q : float,
(FPred p < q)%R -> (q <= p)%R -> (Fexp p <= Fexp q)%Z -> p = q :>R.