intuition.
unfold OMH_G, OMH_G_oc.
fcf_skip.
fcf_simp.
fcf_to_prhl_eq.
simpl.
fcf_inline_first.
fcf_skip.
apply compFold_oc_equiv.
subst.
fcf_inline_first.
fcf_ident_expand_l.
fcf_skip.
fcf_simp.
fcf_spec_ret.
Qed.
Definition OMH_G1 := OMH_G O1.
Definition OMH_G2 := OMH_G O2.

Theorem OMH_G1_equiv:
Pr[OMH_G1] == Pr[G1 _ O1 A1 OMH_G_oc].