Proof using rmri ollpti.
unfold lifted_one_leaderLog_per_term.
intros.
pose proof msg_lift_prop _ one_leaderLog_per_term_invariant _ ltac:(eauto) h h' t ll ll'.
repeat rewrite msg_deghost_spec' in *. auto.
Qed.

Lemma lifted_leaderLog_in_log :
forall net leader ll e,
msg_refined_raft_intermediate_reachable net ->
type (snd (nwState net leader)) = Leader ->
In (currentTerm (snd (nwState net leader)), ll) (leaderLogs (fst (nwState net leader))) ->
In e ll ->
In e (log (snd (nwState net leader))).