Proof using.
unfold raft_net_invariant_reboot, prevLog_leader_sublog, reboot.
intros.  subst. simpl in *.
repeat find_reverse_higher_order_rewrite.
match goal with
| [ H : context [In _ _], H' : In _ _ |- _ ] =>
eapply H with (leader0 := leader) in H'; eauto
end.
- break_exists_exists. intuition.
repeat find_higher_order_rewrite.
break_if; subst; simpl in *; auto.
- repeat find_higher_order_rewrite.
break_if; subst; simpl in *; auto.
discriminate.
- repeat find_higher_order_rewrite.
break_if; subst; simpl in *; auto.
Qed.

(* Specifications: *)
Lemma prevLog_leader_sublog_invariant :
forall net,
raft_intermediate_reachable net ->
prevLog_leader_sublog net.