Proof using.
intros.
unfold handleInput, update_elections_data_input in *.
break_match; repeat break_let; repeat find_inversion;
[eapply_prop msg_refined_raft_net_invariant_timeout|
eapply_prop msg_refined_raft_net_invariant_client_request]; eauto; subst; auto.
Qed.

Theorem msg_refined_raft_net_invariant :
forall P net,
msg_refined_raft_net_invariant_init P ->
msg_refined_raft_net_invariant_client_request P ->
msg_refined_raft_net_invariant_timeout P ->
msg_refined_raft_net_invariant_append_entries P ->
msg_refined_raft_net_invariant_append_entries_reply P ->
msg_refined_raft_net_invariant_request_vote P ->
msg_refined_raft_net_invariant_request_vote_reply P ->
msg_refined_raft_net_invariant_do_leader P ->
msg_refined_raft_net_invariant_do_generic_server P ->
msg_refined_raft_net_invariant_state_same_packet_subset P ->
msg_refined_raft_net_invariant_reboot P ->
msg_refined_raft_intermediate_reachable net ->
P net.