proposition: 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.
proof: Proof. Proof with auto with typeclass_instances. intros m x. apply relative_error_le_conversion... apply Rlt_le. apply Rmult_lt_0_compat. apply Rinv_0_lt_compat. now apply IZR_lt. apply bpow_gt_0. now apply relative_error_N_F2R_emin. Qed.
imports: Coq(ZArith Reals Psatz) Core