Section VotesWithLogSorted.
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}.
Proof using.
unfold refined_raft_net_invariant_init, votesWithLog_sorted.
intros. subst. simpl in *. intuition.
Qed.
Proof using.
unfold update_elections_data_client_request.
intros.
repeat break_match; auto.
Qed.
Proof using.
unfold refined_raft_net_invariant_client_request, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify; simpl in *.
- rewrite votesWithLog_update_elections_data_client_request in *.
eauto.
- eauto.
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.
unfold update_elections_data_timeout.
intros.
repeat break_match; simpl in *; find_inversion; eauto.
Qed.
Proof using si rri.
unfold refined_raft_net_invariant_timeout, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify; simpl in *.
- destruct (votesWithLog (update_elections_data_timeout h0 (nwState net h0)))
using (votesWithLog_update_elections_data_timeout ltac:(eauto)).
+ simpl in *. intuition.
* find_inversion. erewrite handleTimeout_log_same by eauto.
eauto using sorted_host_lifted.
* eauto.
+ eauto.
- eauto.
Qed.
Proof using.
unfold update_elections_data_appendEntries.
intros.
repeat break_match; subst; auto.
Qed.
Proof using.
unfold refined_raft_net_invariant_append_entries, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify; simpl in *.
- rewrite votesWithLog_update_elections_data_AE in *.
eauto.
- eauto.
Qed.
Proof using.
unfold refined_raft_net_invariant_append_entries_reply, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify; simpl in *; eauto.
Qed.
Proof using si rri.
unfold refined_raft_net_invariant_request_vote, votesWithLog_sorted.
intros.
subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify.
- unfold update_elections_data_requestVote in *.
repeat break_match; simpl in *; intuition; repeat find_inversion; eauto;
erewrite handleRequestVote_log; eauto using sorted_host_lifted.
- eauto.
Qed.
Proof using.
unfold update_elections_data_requestVoteReply.
intros.
repeat break_match; simpl; auto.
Qed.
Proof using.
unfold refined_raft_net_invariant_request_vote_reply, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify.
- rewrite votesWithLog_update_elections_data_RVR in *.
eauto.
- eauto.
Qed.
Proof using.
unfold refined_raft_net_invariant_do_leader, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify.
- match goal with
| [ H : _, H' : _ |- _ ] =>
eapply H; rewrite H'; simpl; eauto
end.
- eauto.
Qed.
Proof using.
unfold refined_raft_net_invariant_do_generic_server, votesWithLog_sorted.
intros. subst. simpl in *. find_higher_order_rewrite.
update_destruct_simplify.
- match goal with
| [ H : _, H' : _ |- _ ] =>
eapply H; rewrite H'; simpl; eauto
end.
- eauto.
Qed.

Lemma votesWithLog_sorted_state_same_packet_subset :
refined_raft_net_invariant_state_same_packet_subset votesWithLog_sorted.