Proof using lmi rri.
intros.
find_apply_lem_hyp lift_log_matching.
unfold log_matching, log_matching_hosts in *.
intuition.
split.
- intros.
match goal with
| H : forall _ _, _ <= _ <= _ -> _ |- _ =>
specialize (H h i);
conclude H ltac:(simpl; repeat break_match; simpl in *; repeat find_rewrite; simpl in *;omega)
end.
break_exists_exists; intuition.
simpl in *.
repeat break_match; simpl in *; repeat find_rewrite; simpl in *; auto.
- intros.
cut (eIndex e > 0); intros; try omega.
cut (In e (log (nwState (deghost net) h))); intros; eauto.
simpl in *. repeat break_match. simpl in *. repeat find_rewrite. simpl in *. auto.
Qed.
Ltac start :=
red; unfold leaderLogs_contiguous; intros;
subst; simpl in *; find_higher_order_rewrite;
update_destruct; subst; rewrite_update; eauto; simpl in *.

Lemma leaderLogs_contiguous_init :
refined_raft_net_invariant_init leaderLogs_contiguous.