Notation bpow e := (bpow beta e).

Theorem relative_error_N_FLT_F2R_emin_ex : forall m, let x := F2R (Float beta m emin) in exists eps, (Rabs eps <= /2 * bpow (-prec + 1))%R /\ round beta (FLT_exp emin prec) (Znearest choice) x = (x * (1 + eps))%R.