Notation bpow e := (bpow beta e).

Theorem relative_error_N_FLT_ex : forall x, (bpow (emin + prec - 1) <= Rabs x)%R -> exists eps, (Rabs eps <= /2 * bpow (-prec + 1))%R /\ round beta (FLT_exp emin prec) (Znearest choice) x = (x * (1 + eps))%R.