intuition.
unfold Gi, OMH_G_oc, Gi_oracleMap.
fcf_skip.
fcf_simp.
fcf_to_prhl_eq.
simpl.
fcf_inline_first.
eapply comp_spec_eq_symm.
fcf_skip.
eapply compFold_oc_equiv.
subst.
simpl.
fcf_ident_expand_l.
fcf_inline_first.
fcf_skip.
fcf_simp.
fcf_spec_ret.
Qed.

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