(****************************************************************************  IEEE754  :  Fmin  Laurent Thery  ******************************************************************************)
Require Export Zenum.
Require Export FPred.
Section FMinMax.
Variable b : Fbound.
Variable radix : Z.
Variable precision : nat.
Let FtoRradix := FtoR radix.
Coercion FtoRradix : float >-> R.
Hypothesis radixMoreThanOne : (1 < radix)%Z.
Let radixMoreThanZERO := Zlt_1_O _ (Zlt_le_weak _ _ radixMoreThanOne).
Hint Resolve radixMoreThanZERO: zarith.
Hypothesis precisionNotZero : precision <> 0.
Hypothesis pGivesBound : Zpos (vNum b) = Zpower_nat radix precision.
(* a function that returns a boundd greater than a given nat *)
Definition boundNat (n : nat) := Float 1%nat (digit radix n).

Theorem boundNatCorrect : forall n : nat, (n < boundNat n)%R.
intros n; unfold FtoRradix, FtoR, boundNat in |- *; simpl in |- *.