Proof using.
unfold refined_raft_net_invariant_init, leaderLogs_entries_match,
leaderLogs_entries_match_host, leaderLogs_entries_match_nw.
simpl.
intuition.
Qed.

Lemma entries_match_cons_gt_maxTerm :
forall x xs ys,
sorted xs ->
sorted ys ->
eIndex x > maxIndex xs ->
eTerm x > maxTerm ys ->
entries_match xs ys ->
entries_match (x :: xs) ys.