Section LeaderLogsLogMatching.
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 {lmi : log_matching_interface}.
Context {lltsi : leaderLogs_term_sanity_interface}.
Context {llsi : leaderLogs_sorted_interface}.
Context {si : sorted_interface}.
Context {llsli : leaderLogs_sublog_interface}.
Context {llci : leaderLogs_contiguous_interface}.
Context {taifoi : terms_and_indices_from_one_interface}.
Definition leaderLogs_entries_match_nw (net : network) : Prop :=
forall h llt ll p t src pli plt es ci,
In (llt, ll) (leaderLogs (fst (nwState net h))) ->
In p (nwPackets net) ->
pBody p = AppendEntries t src pli plt es ci ->
(forall e1 e2,
eIndex e1 = eIndex e2 ->
eTerm e1 = eTerm e2 ->
In e1 es ->
In e2 ll ->
(forall e3,
eIndex e3 <= eIndex e1 ->
In e3 es ->
In e3 ll) /\
(pli <> 0 ->
exists e4,
eIndex e4 = pli /\
eTerm e4 = plt /\
In e4 ll)).
Definition leaderLogs_entries_match (net : network) : Prop :=
leaderLogs_entries_match_host net /\
leaderLogs_entries_match_nw net.
Proof using.
unfold refined_raft_net_invariant_init, leaderLogs_entries_match,
leaderLogs_entries_match_host, leaderLogs_entries_match_nw.
simpl.
intuition.
Qed.
Proof using.
unfold entries_match.
intuition; simpl in *; intuition; subst; subst;
try match goal with
| [ H : In _ _ |- _ ] => apply maxTerm_is_max in H; [| solve[auto]]; lia
| [ H : In _ _ |- _ ] => apply maxIndex_is_max in H; [| solve[auto]]; lia
end.
- match goal with
| [ H : _ |- _ ] => solve [eapply H; eauto]
end.
- right. match goal with
| [ H : _ |- _ ] => solve [eapply H; eauto]
end.
Qed.
Proof using.
unfold entries_match.
intuition; simpl in *; intuition; subst; subst;
try solve [
exfalso; try find_apply_hyp_hyp;
match goal with
| [ H : In _ _ |- _ ] => apply maxIndex_is_max in H; [| solve[auto]]; lia
end].
- match goal with
| [ H : _ |- _ ] => solve [eapply H; eauto]
end.
- right. match goal with
| [ H : _ |- _ ] => solve [eapply H; eauto]
end.
Qed.
Proof using.
red.
simpl.
intuition.
Qed.
Proof using si rri.
intros.
pose proof (lift_prop _ logs_sorted_invariant).
find_insterU. conclude_using eauto.
unfold logs_sorted in *. break_and.
unfold logs_sorted_nw in *.
eapply H3.
- unfold deghost. simpl.
apply in_map_iff. eauto.
- simpl. eauto.
Qed.
Proof using si rri.
intros.
pose proof (lift_prop _ logs_sorted_invariant).
find_insterU. conclude_using eauto.
unfold logs_sorted in *. break_and.
unfold logs_sorted_host in *.
find_insterU.
find_rewrite_lem deghost_spec.
eauto.
Qed.
Proof using.
unfold leaderLogs_entries_match_nw.
intros.
eapply_prop_hyp In nwPackets; [|eauto 10].
match goal with
| [ H : _ |- _ ] =>
solve [eapply H; eauto;
repeat find_higher_order_rewrite;
eauto]
end.
Qed.
Proof using.
unfold leaderLogs_entries_match_host.
intuition.
repeat find_higher_order_rewrite. eauto.
Qed.
Proof using.
unfold handleClientRequest.
intros.
repeat break_match; repeat find_inversion; auto.
Qed.
Proof using llsli si llsi lltsi rri.
unfold refined_raft_net_invariant_client_request, leaderLogs_entries_match.
intros.
split.
- { unfold leaderLogs_entries_match_host.
simpl. intuition. subst. repeat find_higher_order_rewrite.
repeat update_destruct_simplify.
- find_rewrite_lem update_elections_data_client_request_leaderLogs.
destruct (log d) using (handleClientRequest_log_ind ltac:(eauto)).
+ eauto.
+ destruct ll.
* apply entries_match_nil.
* { apply entries_match_cons_gt_maxTerm; eauto.
- eauto using lifted_logs_sorted_host.
- eapply leaderLogs_sorted_invariant; eauto.
- lia.
- find_copy_apply_lem_hyp leaderLogs_currentTerm_invariant; auto.
find_copy_apply_lem_hyp leaderLogs_term_sanity_invariant.
unfold leaderLogs_term_sanity in *.
eapply_prop_hyp In In; simpl; eauto. repeat find_rewrite.
simpl in *. lia.
}
- destruct (log d) using (handleClientRequest_log_ind ltac:(eauto)).
+ eauto.
+ apply entries_match_cons_sublog; eauto.
* eauto using lifted_logs_sorted_host.
* eapply leaderLogs_sorted_invariant; eauto.
* lia.
* intros.
eapply leaderLogs_sublog_invariant; eauto.
simpl in *. congruence.
- find_rewrite_lem update_elections_data_client_request_leaderLogs.
eauto.
- eauto.
}
- eapply leaderLogs_entries_match_nw_packet_set with (net:=net); intuition.
+ find_apply_hyp_hyp. intuition eauto.
erewrite handleClientRequest_no_send with (ms := l) in * by eauto.
simpl in *. intuition.
+ simpl. subst. find_higher_order_rewrite.
rewrite update_fun_comm. simpl.
rewrite update_fun_comm. simpl.
rewrite update_elections_data_client_request_leaderLogs.
now rewrite update_nop_ext' by auto.
Qed.
Proof using.
unfold refined_raft_net_invariant_timeout, leaderLogs_entries_match.
intuition.
- eapply leaderLogs_entries_match_host_state_same; eauto;
simpl; intros; subst; find_higher_order_rewrite;
repeat update_destruct_simplify; rewrite_update; auto;
try rewrite update_elections_data_timeout_leaderLogs;
try erewrite handleTimeout_log_same by eauto; eauto.
- eapply leaderLogs_entries_match_nw_packet_set with (net:=net); intuition.
+ simpl in *. find_apply_hyp_hyp.  intuition.
do_in_map. subst. simpl in *.
exfalso. eapply handleTimeout_not_is_append_entries; eauto 10.
+ simpl. repeat find_higher_order_rewrite.
rewrite update_fun_comm. simpl.
rewrite update_fun_comm. simpl.
rewrite update_elections_data_timeout_leaderLogs.
rewrite update_nop_ext'; auto.
Qed.
Proof using lmi rri.
intros.
pose proof (lift_prop _ log_matching_invariant).
find_insterU. conclude_using eauto.
auto.
Qed.

Lemma lifted_log_matching_host :
forall net,
refined_raft_intermediate_reachable net ->
(forall h h',
entries_match (log (snd (nwState net h))) (log (snd (nwState net h')))) /\
(forall h i,
1 <= i <= maxIndex (log (snd (nwState net h))) ->
exists e, eIndex e = i /\ In e (log (snd (nwState net h)))) /\
(forall h e,
In e (log (snd (nwState net h))) -> eIndex e > 0).