intros x y H' H'0.
apply lt_IZR.
apply (Rlt_monotony_contra_exp radix) with (z := Fexp x);
auto with real arith.
pattern (Fexp x) at 2 in |- *; rewrite H'0; auto.
Qed.

(* Specifications: *)
Theorem Rle_Fexp_eq_Zle :
forall x y : float, (x <= y)%R -> Fexp x = Fexp y -> (Fnum x <= Fnum y)%Z.