Proof using.
unfold entries_match. intros.
intuition.
- simpl in *. intuition.
+ unfold log_matching_hosts in *.
subst. simpl in *. contradict_leader_sublog.
+ subst. simpl in *.
contradict_leader_sublog.
+ subst. simpl in *. contradict_maxIndex.
+ unfold log_matching_hosts in *. intuition.
use_entries_match.
- simpl in *. intuition.
+ subst. simpl in *.
contradict_leader_sublog.
+ unfold log_matching_hosts in *. intuition.
right. use_entries_match.
Qed.

Lemma leader_sublog_weaken_host :
forall net,
leader_sublog_invariant net ->
leader_sublog_host_invariant net.