apply le_IZR.
apply (Rle_monotony_contra_exp radix) with (z := Fexp p);
auto with real arith.
simpl in |- *; rewrite Rmult_0_l; auto.
Qed.

Theorem LeFnumZERO : forall x : float, (0 <= Fnum x)%Z -> (0 <= x)%R.
intros x H'; unfold FtoRradix, FtoR in |- *.