Proof using rmri tsi.
intros.
enough (no_entries_past_current_term_host (deghost (mgv_deghost net))) by
(unfold no_entries_past_current_term_host, lifted_no_entries_past_current_term_host, deghost, mgv_deghost in *;
simpl in *;
repeat break_match; simpl in *; auto).
apply msg_lift_prop_all_the_way; eauto.
intros.
eapply no_entries_past_current_term_invariant; eauto.
Qed.

Lemma all_the_way_deghost_spec :
forall (net : ghost_log_network) h,
snd (nwState net h) = nwState (deghost (mgv_deghost net)) h.