(****************************************************************************  IEEE754  :  Finduct  Laurent Thery  ***************************************************************************** Define an induction principle on float*)
Require Export FPred.
Section finduct.
Variable b : Fbound.
Variable radix : Z.
Variable precision : nat.
Let FtoRradix := FtoR radix.
Local 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.
Definition Fweight (p : float) :=
(Fnum p + Fexp p * Zpower_nat radix precision)%Z.

Theorem FweightLt :
forall p q : float,
Fcanonic radix b p ->
Fcanonic radix b q -> (0 <= p)%R -> (p < q)%R -> (Fweight p < Fweight q)%Z.