Proof using rlmli rmri.
intros.
unfold lifted_entries_match; intros.
find_eapply_lem_hyp msg_lift_prop;
[|intros; eapply (entries_match_invariant ltac:(eauto) h h'); eauto].
simpl in *.
repeat break_match; simpl in *; auto.
Qed.
Definition lifted_no_entries_past_current_term_host net :=
forall (h : name) e,
In e (log (snd (nwState net h))) ->
eTerm e <= currentTerm (snd (nwState net h)).

Lemma lifted_no_entries_past_current_term_host_invariant :
forall (net : @network _ raft_msg_refined_multi_params),
msg_refined_raft_intermediate_reachable net ->
lifted_no_entries_past_current_term_host net.