Notation bpow e := (bpow beta e).

Lemma error_N_FLT : forall (emin prec : Z), (0 < prec)%Z -> forall (choice : Z -> bool), forall (x : R), exists eps eta : R, (Rabs eps <= /2 * bpow (-prec + 1))%R /\ (Rabs eta <= /2 * bpow emin)%R /\ (eps * eta = 0)%R /\ (round beta (FLT_exp emin prec) (Znearest choice) x = x * (1 + eps) + eta)%R.