Section StateMachineSafetyProof.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {rri : raft_refinement_interface}.
Context {si : sorted_interface}.
Context {lmi : log_matching_interface}.
Context {smspi : state_machine_safety'interface}.
Context {rlmli : refined_log_matching_lemmas_interface}.
Context {pllsi : prevLog_leader_sublog_interface}.
Context {ctgt0 : current_term_gt_zero_interface}.
Context {lalcii : lastApplied_le_commitIndex_interface}.
Context {miaei : match_index_all_entries_interface}.
Context {lhlli : leaders_have_leaderLogs_interface}.
Context {lci : leader_completeness_interface}.
Context {lsi : leader_sublog_interface}.
Context {taifoli : terms_and_indices_from_one_log_interface}.
Context {glci : ghost_log_correct_interface}.
Context {lphogli : log_properties_hold_on_ghost_logs_interface}.
Context {glemi : ghost_log_entries_match_interface}.
Context {tci : transitive_commit_interface}.
Context {tsi : term_sanity_interface}.
Context {lhllsi : leaders_have_leaderLogs_strong_interface}.
Context {ollpti : one_leaderLog_per_term_interface}.
Context {rmri : raft_msg_refinement_interface}.
Proof using.
intros.
unfold deghost in *. simpl in *. do_in_map.
subst. eexists; eauto.
Qed.
Proof using.
intros. unfold state_machine_safety in *. intuition.
- unfold state_machine_safety_host. intros.
do 2 eapply_prop_hyp commit_recorded_committed commit_recorded.
unfold state_machine_safety' in *. intuition. eauto.
- unfold state_machine_safety_nw. intros.
eapply_prop_hyp commit_recorded_committed commit_recorded.
unfold state_machine_safety', state_machine_safety_nw' in *. intuition.
find_apply_lem_hyp exists_deghost_packet. break_exists.
intuition. subst. simpl in *. repeat break_match. simpl in *.
subst. eapply_prop_hyp In In; repeat find_rewrite; simpl; eauto.
Qed.
Definition ghost_log_network : Type := @network _ raft_msg_refined_multi_params.
Definition ghost_log_packet : Type := @packet _ raft_msg_refined_multi_params.
Definition lifted_maxIndex_sanity (net : ghost_log_network) : Prop :=
(forall h,
lastApplied (snd (nwState net h)) <= maxIndex (log (snd (nwState net h)))) /\
(forall h, commitIndex (snd (nwState net h)) <= maxIndex (log (snd (nwState net h)))).
Proof using.
unfold msg_refined_raft_net_invariant_init, lifted_maxIndex_sanity, maxIndex_lastApplied, maxIndex_commitIndex.
intuition.
Qed.
Proof using.
unfold handleClientRequest.
intros.
repeat break_match; find_inversion; auto.
Qed.
Proof using.
intros.
destruct (log st') using (handleClientRequest_log_ind ltac:(eauto)).
- auto.
- simpl in *. break_and.
destruct (log st); simpl in *.
+ lia.
+ find_insterU. conclude_using eauto. intuition.
Qed.
Proof using si rri.
intros.
pose proof (lift_prop _ logs_sorted_invariant).
find_insterU. conclude_using eauto.
unfold logs_sorted, logs_sorted_host in *. break_and.
unfold deghost in *. simpl in *. break_match. eauto.
Qed.
Proof using rmri si rri.
intros net0 ??.
rewrite <- msg_deghost_spec with (net := net0).
eapply msg_lift_prop.
- auto using lifted_sorted_host.
- auto.
Qed.

Lemma lifted_sorted_network :
forall net p t n pli plt es ci,
refined_raft_intermediate_reachable net ->
In p (nwPackets net) ->
pBody p = AppendEntries t n pli plt es ci ->
sorted es.