Proof using.
unfold msg_refined_raft_net_invariant_state_same_packet_subset,
lifted_maxIndex_sanity, maxIndex_lastApplied, maxIndex_commitIndex.
intuition; find_reverse_higher_order_rewrite; auto.
Qed.

Lemma lifted_maxIndex_sanity_reboot :
msg_refined_raft_net_invariant_reboot lifted_maxIndex_sanity.