Proof using rmri.
unfold lifted_directly_committed, directly_committed.
intuition.
break_exists_exists.
intuition.
find_apply_hyp_hyp.
find_rewrite_lem msg_deghost_spec. auto.
Qed.

Lemma lifted_committed_committed :
forall net e t,
lifted_committed net e t ->
committed (mgv_deghost net) e t.