unfold negligible.
intuition.
destruct (H c).
exists x.
intuition.
eapply H0.
intuition.
rewrite H2.
rewrite Def_equiv_2W.
rewrite ratMult_comm.
eapply ratMult_small_le.
eapply rat_le_1.
simpl.
omega.
Qed.

Theorem TwoWorlds_equiv_b :
negligible (fun eta => | Pr[StandardDef_G eta] - 1 / 2 |) ->
negligible (fun eta => (| Pr[f eta false] - Pr[f eta true] |)).