Section Float_prop.
Variable beta : radix.
Notation bpow e := (bpow beta e).

Theorem F2R_prec_normalize :
forall m e e' p : Z,
(Z.abs m < Zpower beta p)%Z ->
(bpow (e' - 1)%Z <= Rabs (F2R (Float beta m e)))%R ->
F2R (Float beta m e) = F2R (Float beta (m * Zpower beta (e - e' + p)) (e' - p)).