intuition.
unfold Gi_oracleMap, Gi_oracleMap'.
fcf_skip.
fcf_simp.
fcf_skip.
cutrewrite (l = (firstn i l ++ skipn i l)).
eapply eqRat_trans.
eapply compFold_app.
fcf_skip.
rewrite firstn_skipn.
reflexivity.
fcf_simp.
fcf_ident_expand_l.
fcf_to_prhl_eq.
rewrite firstn_skipn.
fcf_skip.
eapply (compFold_spec' (fun a b c d => a = b /\ snd c = snd d /\ l0++ (fst d) = (fst c)));
intuition.
simpl.
eapply app_nil_r.
simpl in *.
subst.
destruct d.
simpl in *.
subst.
unfold Oi.
inversion H2; clear H2; subst.
fcf_inline_first.
fcf_skip.
fcf_simp.
fcf_spec_ret.
simpl.
rewrite app_assoc.
trivial.
fcf_simp.
simpl in H3.
intuition.
subst.
fcf_spec_ret.
rewrite firstn_skipn.
trivial.
Qed.

Theorem OMH_G_i_equiv :
forall i,
Pr[Gi_oracleMap' i] == Pr[OMH_G_i i].