Proof using aeli rri.
intros.
apply (lower_prop lowered_appendEntries_leader); auto.
intros.
find_apply_lem_hyp append_entries_leader_invariant.
unfold lowered_appendEntries_leader, appendEntries_leader in *.
intros. simpl in *.
repeat break_match. simpl in *.
do_in_map. subst. simpl in *.
match goal with
| H : ?nwState  ?h = (?gd, ?d) |- _ =>
replace gd with (fst (nwState h)) in * by (rewrite H; reflexivity);
replace d with (snd (nwState h)) in * by (rewrite H; reflexivity);
clear H
end.
eapply_prop_hyp AppendEntries AppendEntries; eauto.
Qed.

Theorem append_entries_reply_sublog_invariant :
forall net,
raft_intermediate_reachable net ->
append_entries_reply_sublog net.