pattern a at 2 in |- *; rewrite <- (Fopp_Fopp a).
unfold FtoRradix in |- *; repeat rewrite Fopp_correct.
apply Ropp_lt_contravar.
rewrite <- Fopp_correct; auto with float.
Qed.

(* Specifications: *)
Theorem R0RltRlePred : forall x : float, (0 < x)%R -> (0 <= FPred x)%R.
intros x H'; rewrite FPredFopFSucc.