induction x1; inversion 1; intuition; simpl in *.
subst.
destruct a.
destruct a2.
simpl in *.
subst.
destruct p.
simpl.
destruct (eqb a0 b0 ); intuition.
Qed.

Theorem G2_1_2_equiv :
Pr[G2_1] == Pr[G2_2].