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

(* Specifications: *)
Lemma directly_committed_lifted_directly_committed :
forall net e,
directly_committed (mgv_deghost net) e ->
lifted_directly_committed net e.