unfold FtoRradix in |- *; repeat rewrite Fopp_correct.
replace 0%R with (-0)%R; auto with real.
apply Ropp_le_contravar.
apply R0RltRleSucc; auto.
unfold FtoRradix in |- *; repeat rewrite Fopp_correct.
replace 0%R with (-0)%R; auto with real.
Qed.

Theorem FPredProp :
forall x y : float,
Fcanonic radix b x -> Fcanonic radix b y -> (x < y)%R -> (x <= FPred y)%R.