Proof using rmri.
unfold msg_refined_raft_net_invariant_state_same_packet_subset, commit_invariant.
intuition.
- unfold commit_invariant_host in *. intros.
repeat find_reverse_higher_order_rewrite.
destruct net, net'. simpl in *.
eapply lifted_committed_ext; [|eauto]. simpl. auto.
- unfold commit_invariant_nw in *. intros.
find_apply_hyp_hyp.
destruct net, net'. simpl in *.
eapply lifted_committed_ext'; [|eauto]. auto.
Qed.

Lemma reboot_preserves_committed :
forall (net net' : ghost_log_network) h e t,
(forall h', nwState net' h' = update name_eq_dec (nwState net) h (fst (nwState net h), reboot (snd (nwState net h))) h') ->
lifted_committed net e t ->
lifted_committed net' e t.