(****************************************************************************  IEEE754  :  Fodd  Laurent Thery  ******************************************************************************)
Require Export Fmin.
Section FOdd.
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 precisionGreaterThanOne : 1 < precision.
Hypothesis pGivesBound : Zpos (vNum b) = Zpower_nat radix precision.
(* We define the parity predicates*)
Definition Even (z : Z) : Prop := exists z1 : _, z = (2 * z1)%Z.
Definition Odd (z : Z) : Prop := exists z1 : _, z = (2 * z1 + 1)%Z.

Theorem OddSEven : forall n : Z, Odd n -> Even (Zsucc n).
intros n H'; case H'; intros m H'1; exists (Zsucc m).