Section Odd_propbis.
Variable beta : radix.
Hypothesis Even_beta: Z.even (radix_val beta)=true.
Variable emin prec:Z.
Variable choice:Z->bool.
Hypothesis prec_gt_1: (1 < prec)%Z.
Notation format := (generic_format beta (FLT_exp emin prec)).
Notation round_flt :=(round beta (FLT_exp emin prec) (Znearest choice)).
Notation cexp_flt := (cexp beta (FLT_exp emin prec)).
Notation fexpe k := (FLT_exp (emin-k) (prec+k)).

Lemma Zrnd_odd_plus': forall x y,
(exists n:Z, exists e:Z, (x = IZR n*bpow beta e)%R /\ (1 <= e)%Z) ->
(IZR (Zrnd_odd (x+y)) = x+IZR (Zrnd_odd y))%R.