Section Fbounded_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.
Local Coercion FtoRradix : float >-> R.
Coercion Z_of_N: N >-> Z.
Record Fbound : Set := Bound {vNum : positive; dExp : N}.
Definition Fbounded (b : Fbound) (d : float) :=
(Z.abs (Fnum d) < Zpos (vNum b))%Z /\ (- dExp b <= Fexp d)%Z.

Theorem FboundedNum :
forall (b : Fbound) (p : float),
Fbounded b p -> (Z.abs (Fnum p) < Zpos (vNum b))%Z.