Section Fcore_rnd_odd.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable fexp : Z -> Z.
Context { valid_exp : Valid_exp fexp }.
Context { exists_NE_ : Exists_NE beta fexp }.
Notation format := (generic_format beta fexp).
Notation canonical := (canonical beta fexp).
Notation cexp := (cexp beta fexp).
Definition Rnd_odd_pt (x f : R) :=
format f /\ ((f = x)%R \/
((Rnd_DN_pt format x f \/ Rnd_UP_pt format x f) /\
exists g : float beta, f = F2R g /\ canonical g /\ Z.even (Fnum g) = false)).
Definition Rnd_odd (rnd : R -> R) :=
forall x : R, Rnd_odd_pt x (rnd x).

Theorem Rnd_odd_pt_opp_inv :   forall x f : R,
Rnd_odd_pt (-x) (-f) -> Rnd_odd_pt x f.