(****************************************************************************  IEEE754  :  Fnorm  Laurent Thery  &  Sylvie Boldo  ******************************************************************************)
Require Export Fbound.
Section Fnormalized_Def.
Variable radix : Z.
Hypothesis radixMoreThanOne : (1 < radix)%Z.
Let radixMoreThanZERO := Zlt_1_O _ (Zlt_le_weak _ _ radixMoreThanOne).
Hint Resolve radixMoreThanZERO: zarith.
Let FtoRradix := FtoR radix.
Coercion FtoRradix : float >-> R.
Variable b : Fbound.
Definition Fnormal (p : float) :=
Fbounded b p /\ (Zpos (vNum b) <= Zabs (radix * Fnum p))%Z.

Theorem FnormalBounded : forall p : float, Fnormal p -> Fbounded b p.
intros p H; case H; auto.