Proof using rmri lalcii smspi rri.
unfold msg_refined_raft_net_invariant_do_generic_server', everything.
intuition.
- eapply lifted_maxIndex_sanity_do_generic_server; eauto.
- eapply commit_invariant_do_generic_server; eauto.
- apply state_machine_safety_deghost.
+ apply commit_invariant_lower_commit_recorded_committed. auto.
eapply commit_invariant_do_generic_server; eauto.
+ apply state_machine_safety'_invariant. auto using msg_simulation_1.
Qed.

Lemma directly_committed_state_same :
forall net net' e,
(forall h, nwState net' h = nwState net h) ->
directly_committed net e ->
directly_committed net' e.