Notation bpow e := (bpow beta e).

Theorem relative_error_N_F2R_emin_ex : forall m, let x := F2R (Float beta m emin) in exists eps, (Rabs eps <= /2 * bpow (-p + 1))%R /\ round beta fexp (Znearest choice) x = (x * (1 + eps))%R.