Notation bpow e := (bpow beta e).

Theorem F2R_prec_normalize : forall m e e' p : Z, (Zabs 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)).