Proof using.
red. unfold CandidateEntries.
intros.
intuition.
- unfold candidateEntries_host_invariant in *.
intros.
repeat find_reverse_higher_order_rewrite.
apply candidateEntries_ext with (sigma := nwState net); eauto.
- unfold candidateEntries_nw_invariant in *.
intros.
find_apply_hyp_hyp.
eapply_prop_hyp In In; eauto.
apply candidateEntries_ext with (sigma := nwState net); eauto.
Qed.

Lemma reboot_log_same :
forall d,
log (reboot d) = log d.