rewrite G2_1_equiv.
rewrite G2_1_2_equiv.
rewrite G2_2_3_equiv.
rewrite <- G2_5_equiv.
rewrite <- G2_4_5_equiv.
eapply G2_3_4_close.
Qed.

Theorem G2_equiv :
Pr[G2] == Pr[PRF_G_B ({0, 1}^c) _ _ A].