Section OneLeaderLogPerTerm.
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 {llvwli : leaderLogs_votesWithLog_interface}.
Context {vci : votes_correct_interface}.
Context {cci : cronies_correct_interface}.
Context {vvci : votes_votesWithLog_correspond_interface}.
Context {lltsi : leaderLogs_term_sanity_interface}.
Ltac start :=
red; unfold one_leaderLog_per_term; simpl; intros.
Ltac start_update :=
start;
repeat find_higher_order_rewrite;
repeat (update_destruct; subst; rewrite_update);
[| | |eauto].
Proof using.
start. contradiction.
Qed.
Proof using.
unfold one_leaderLog_per_term. intros.
repeat find_higher_order_rewrite;
repeat (update_destruct; subst; rewrite_update);
simpl in *; repeat find_rewrite; eauto.
Qed.
Ltac start_unchanged :=
red; intros; eapply one_leaderLog_per_term_unchanged; eauto; subst.
(* solve invariant by lemma which shows leader logs do not change *)
Ltac unchanged lem :=
start_unchanged; apply lem.
Proof using.
unchanged update_elections_data_client_request_leaderLogs.
Qed.
Proof using.
unchanged update_elections_data_timeout_leaderLogs.
Qed.
Proof using.
unchanged update_elections_data_appendEntries_leaderLogs.
Qed.
Proof using.
start_unchanged. auto.
Qed.
Proof using.
unchanged leaderLogs_update_elections_data_requestVote.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros.
repeat break_match; auto.
simpl in *. intuition.
find_inversion. right.
unfold handleRequestVoteReply in *.
repeat break_match; simpl in *; intuition; try congruence;
break_if; try congruence; do_bool; eauto using le_antisym.
Qed.
Proof using.
unfold wonElection. intros. find_apply_lem_hyp leb_true_le. lia.
Qed.
Proof using one_node_params.
intros. eapply pigeon with (l := nodes).
- apply name_eq_dec.
- intros. apply (@all_names_nodes _ multi_params).
- intros. apply (@all_names_nodes _ multi_params).
- apply (@no_dup_nodes _ multi_params).
- assumption.
- assumption.
- apply div2_correct; assumption.
Qed.
Proof using vvci cci vci llvwli.
intros. unfold not in *. find_false.
simpl in *. find_apply_lem_hyp update_elections_data_requestVoteReply_leaderLogs'.
intro_refined_invariant leaderLogs_votesWithLog_invariant.
break_or_hyp; repeat (apply_prop_hyp leaderLogs_votesWithLog In; break_exists).
- assert (exists h, In h x /\ In h x0) by (apply pigeon_nodes; intuition).
break_exists; break_and.
do 2 (find_apply_hyp_hyp; break_exists; break_and).
intro_refined_invariant votes_votesWithLog_correspond_invariant.
do 2 (apply_prop_hyp votes_votesWithLog In).
intro_refined_invariant votes_correct_invariant.
eauto.
- assert (exists h, In h x /\ In h (dedup name_eq_dec (pSrc p :: votesReceived (snd (nwState net (pDst p)))))).
{ eapply pigeon_nodes.
- intuition.
- apply NoDup_dedup.
- intuition.
- apply wonElection_length; intuition. }
break_exists. break_and.
find_apply_hyp_hyp; break_exists; break_and.
intro_refined_invariant votes_votesWithLog_correspond_invariant.
apply_prop_hyp votes_votesWithLog In.
find_apply_lem_hyp in_dedup_was_in.
simpl in *.
intro_refined_invariant cronies_correct_invariant.
intro_refined_invariant votes_correct_invariant.
break_or_hyp; eauto.
Qed.
Proof using lltsi vvci cci vci llvwli.
start. repeat find_higher_order_rewrite. repeat (update_destruct; rewrite_update).
- split; [subst; auto|].
find_copy_eapply_lem_hyp leaderLogs_update_elections_data_RVR; [|eauto].
pose proof H.
eapply @leaderLogs_update_elections_data_RVR with (ll := ll) in H; [|eauto].
intro_refined_invariant leaderLogs_currentTerm_sanity_candidate_invariant.
intuition.
+ match goal with
| [ h: _ |- _ ] => solve[eapply h; eauto]
end.
+ apply_prop_hyp leaderLogs_currentTerm_sanity_candidate nwState; auto.
find_copy_apply_lem_hyp handleRequestVoteReply_type. intuition; unfold raft_data in *; simpl in *.
* subst. repeat find_rewrite. discriminate.
* find_apply_lem_hyp lt_asym. congruence.
* subst. repeat find_rewrite. find_apply_lem_hyp lt_irrefl. contradiction.
+ apply_prop_hyp leaderLogs_currentTerm_sanity_candidate nwState; auto.
find_copy_apply_lem_hyp handleRequestVoteReply_type. intuition; unfold raft_data in *; simpl in *.
* subst. repeat find_rewrite. discriminate.
* find_apply_lem_hyp lt_asym. congruence.
* subst. repeat find_rewrite. find_apply_lem_hyp lt_irrefl. contradiction.
+ subst. auto.
- exfalso. eapply contradiction_case; eauto.
- exfalso. eapply contradiction_case; eauto.
- eauto.
Qed.
Proof using.
start_unchanged. find_rewrite. auto.
Qed.
Proof using.
start_unchanged. find_rewrite. auto.
Qed.
Proof using.
start. repeat find_reverse_higher_order_rewrite. eauto.
Qed.

Lemma one_leaderLog_per_term_reboot :
refined_raft_net_invariant_reboot one_leaderLog_per_term.