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.

Lemma pigeon_nodes :
forall (q1 q2 : list name),
NoDup q1 ->
NoDup q2 ->
length q1 > div2 (length nodes) ->
length q2 > div2 (length nodes) ->
exists v, In v q1 /\ In v q2.