Proof using rmri.
unfold lifted_committed, committed.
intros.
break_exists_exists.
rewrite msg_deghost_spec.
intuition auto using lifted_directly_committed_directly_committed.
Qed.

(* Specifications: *)
Lemma committed_lifted_committed :
forall net e t,
committed (mgv_deghost net) e t ->
lifted_committed net e t.