Proof using.
unfold refined_raft_net_invariant_state_same_packet_subset, match_index_all_entries_inv.
simpl. intros. break_and. split.
- unfold match_index_all_entries in *.
intros.
repeat find_reverse_higher_order_rewrite.
eauto.
- unfold match_index_all_entries_nw in *.
intros.
find_apply_hyp_hyp.
repeat find_reverse_higher_order_rewrite.
eauto.
Qed.

Lemma match_index_all_entries_reboot :
refined_raft_net_invariant_reboot match_index_all_entries_inv.