(****************************************************************************  IEEE754  :  ClosestProp  Laurent Thery, Sylvie Boldo  ******************************************************************************)
Require Export FroundProp.
Require Export Closest.
Section Fclosestp2.
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 precisionGreaterThanOne : 1 < precision.
Hypothesis pGivesBound : Zpos (vNum b) = Zpower_nat radix precision.

Theorem ClosestOpp :
forall (p : float) (r : R),
Closest b radix r p -> Closest b radix (- r) (Fopp p).