Fprop

# Library Fprop

`Require Export Fbound.
Section Fprop.
Variable radix : Z.
Hypothesis radixMoreThanOne : (1 < radix)%Z.
Coercion Local FtoRradix := FtoR radix.
Variable b : Fbound.
Theorem SterbenzAux :
forall x y : float,
Fbounded b x ->
Fbounded b y ->
(y <= x)%R -> (x <= 2%nat * y)%R -> Fbounded b (Fminus radix x y).
Theorem Sterbenz :
forall x y : float,
Fbounded b x ->
Fbounded b y ->
(/ 2%nat * y <= x)%R -> (x <= 2%nat * y)%R -> Fbounded b (Fminus radix x y).
Theorem BminusSameExpAux :
forall x y : float,
Fbounded b x ->
Fbounded b y ->
(0 <= y)%R -> (y <= x)%R -> Fexp x = Fexp y -> Fbounded b (Fminus radix x y).
Theorem BminusSameExp :
forall x y : float,
Fbounded b x ->
Fbounded b y ->
(0 <= x)%R -> (0 <= y)%R -> Fexp x = Fexp y -> Fbounded b (Fminus radix x y).
Theorem BminusSameExpNeg :
forall x y : float,
Fbounded b x ->
Fbounded b y ->
(x <= 0)%R -> (y <= 0)%R -> Fexp x = Fexp y -> Fbounded b (Fminus radix x y).
End Fprop.
Hint Resolve Sterbenz BminusSameExp BminusSameExpNeg: float.
`