Proof using rmri.
unfold lifted_committed, committed.
intros.
break_exists_exists.
find_rewrite_lem msg_deghost_spec.
intuition auto using directly_committed_lifted_directly_committed.
Qed.

Lemma msg_deghost_spec' :
forall base multi ghost
(net : @network (@mgv_refined_base_params base)
(@mgv_refined_multi_params base multi ghost)) h,
nwState (mgv_deghost net) h = nwState net h.