Section SpecLemmas.
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}.
Proof using.
unfold update_elections_data_requestVote.
intros.
repeat break_match; repeat tuple_inversion; intuition;
simpl in *; intuition;
tuple_inversion; intuition.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros. repeat break_match; repeat tuple_inversion; intuition.
Qed.
Proof using.
intros. unfold update_elections_data_appendEntries.
repeat break_match; auto.
Qed.
Proof using.
unfold update_elections_data_timeout, handleTimeout, tryToBecomeLeader.
intros.
repeat break_match; simpl in *; intuition; repeat tuple_inversion; intuition.
Qed.
Proof using.
unfold handleTimeout, tryToBecomeLeader.
intros. repeat break_match; repeat tuple_inversion; simpl in *; auto; lia.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros. repeat break_match; repeat tuple_inversion; intuition.
Qed.
Proof using.
unfold update_elections_data_requestVote.
intros.
repeat break_match; repeat tuple_inversion; do_bool; intuition;
simpl in *; intuition; do_bool; try discriminate; intuition try congruence.
lia.
Qed.
Proof using.
unfold update_elections_data_requestVote.
intros.
repeat break_match; repeat tuple_inversion; simpl; auto.
Qed.
Proof using.
unfold update_elections_data_timeout, handleTimeout, tryToBecomeLeader.
intros.
repeat break_match; simpl in *; intuition; repeat tuple_inversion;
intuition (auto; congruence).
Qed.
Proof using.
unfold update_elections_data_timeout.
intros. repeat break_match; simpl in *; intuition; repeat tuple_inversion; intuition.
Qed.
Proof using.
intros. unfold update_elections_data_client_request.
repeat break_match; auto.
Qed.
Proof using.
intros. unfold update_elections_data_client_request.
repeat break_match; auto.
Qed.
Proof using.
unfold update_elections_data_client_request.
intros. repeat break_match; repeat tuple_inversion; intuition.
Qed.
Proof using.
unfold update_elections_data_timeout.
intros. repeat break_match; simpl in *; intuition; repeat tuple_inversion; intuition.
Qed.
Proof using.
intros. unfold update_elections_data_appendEntries.
repeat break_match; auto.
Qed.
Proof using.
unfold update_elections_data_appendEntries.
intros. repeat break_match; repeat tuple_inversion; intuition.
Qed.
Proof using.
unfold update_elections_data_requestVote.
intros.
repeat break_match; repeat tuple_inversion; intuition;
simpl in *; intuition;
tuple_inversion; intuition.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros. repeat break_match; repeat tuple_inversion; intuition.
Qed.
Proof using.
intros.
unfold update_elections_data_requestVoteReply.
break_match; simpl in *; auto.
Qed.
Proof using.
unfold update_elections_data_client_request in *.
intros. repeat break_match; repeat find_inversion; auto.
Qed.
Proof using.
unfold update_elections_data_timeout.
intros.
repeat break_match; auto.
Qed.
Proof using.
unfold update_elections_data_appendEntries.
intros. repeat break_match; auto.
Qed.
Proof using.
unfold update_elections_data_requestVote.
intros.
repeat break_match; repeat find_inversion; auto.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros.
repeat break_match; repeat find_inversion; intuition.
simpl in *. intuition.
find_inversion. intuition.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros.
repeat break_match; repeat find_inversion; intuition.
simpl in *. intuition.
Qed.
Proof using.
intros.
unfold update_elections_data_client_request.
repeat break_match; repeat find_inversion; auto.
simpl.
find_copy_apply_lem_hyp handleClientRequest_log.
intuition.
- repeat find_rewrite. do_bool. lia.
- right.  break_exists_exists. intuition.
congruence.
Qed.
Proof using.
intros.
unfold update_elections_data_client_request.
unfold handleClientRequest in *.
repeat break_match; repeat tuple_inversion; auto.
- discriminate.
- do_bool. find_rewrite. lia.
- do_bool. find_rewrite. lia.
- simpl in *. right. intuition. exists e. find_inversion. simpl. intuition.
- simpl in *. do_bool. lia.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros.
repeat break_match; auto.
Qed.
Proof using.
intros. unfold handleAppendEntries in *.
repeat break_match; find_inversion; simpl in *; intuition; eauto using advanceCurrentTerm_log.
Qed.
Proof using.
intros.
unfold update_elections_data_appendEntries in *.
repeat break_match; subst; simpl in *; auto.
find_apply_lem_hyp handleAppendEntriesReply_entries. subst.
do_in_map. do_in_app. subst. intuition.
- do_in_map. subst. simpl in *. auto.
- left. apply in_map_iff. eexists; eauto.
Qed.
Proof using.
intros.
unfold update_elections_data_appendEntries in *.
repeat break_match; subst; simpl in *; auto.
find_apply_lem_hyp handleAppendEntriesReply_entries.
intuition. subst.
do_in_app. intuition.
do_in_map. repeat find_inversion. subst. simpl in *. auto.
Qed.
Proof using.
intros.
unfold update_elections_data_appendEntries in *.
repeat break_match; subst; simpl in *; auto.
unfold handleAppendEntries, advanceCurrentTerm in *.
repeat break_match; simpl in *; repeat find_inversion; do_bool; simpl in *; auto;
try (do_in_app; intuition; do_in_map;  repeat find_inversion; subst; simpl in *; auto);
find_eapply_lem_hyp Nat.le_antisymm; eauto.
Qed.

Lemma update_elections_data_appendEntries_log_allEntries :
forall h st t n pli plt es ci st' h' ps,
handleAppendEntries h (snd st) t n pli plt es ci = (st', ps) ->
(log st' = log (snd st) /\
allEntries (update_elections_data_appendEntries h st t h' pli plt es ci) =
allEntries (fst st))  \/
(allEntries (update_elections_data_appendEntries h st t h' pli plt es ci) =
(map (fun e => (t, e)) es) ++ allEntries (fst st) /\
((currentTerm st' = t /\ log st' = log (snd st) /\ haveNewEntries (snd st) es = false) \/
(currentTerm st' = t /\ currentTerm (snd st) <= t /\ es <> [] /\ pli = 0 /\ log st' = es) \/
(currentTerm st' = t /\ currentTerm (snd st) <= t /\ es <> [] /\ pli <> 0 /\ exists e,
In e (log (snd st)) /\
eIndex e = pli /\
eTerm e = plt) /\
log st' = es ++ (removeAfterIndex (log (snd st)) pli))).