Notation bpow e := (bpow beta e).

Theorem relative_error_N_FLT_round_F2R_emin : forall m, let x := F2R (Float beta m emin) in (Rabs (round beta (FLT_exp emin prec) (Znearest choice) x - x) <= /2 * bpow (-prec + 1) * Rabs (round beta (FLT_exp emin prec) (Znearest choice) x))%R.