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

Theorem refined_raft_net_invariant' :
forall P net,
refined_raft_net_invariant_init P ->
refined_raft_net_invariant_client_request' P ->
refined_raft_net_invariant_timeout' P ->
refined_raft_net_invariant_append_entries' P ->
refined_raft_net_invariant_append_entries_reply' P ->
refined_raft_net_invariant_request_vote' P ->
refined_raft_net_invariant_request_vote_reply' P ->
refined_raft_net_invariant_do_leader' P ->
refined_raft_net_invariant_do_generic_server' P ->
refined_raft_net_invariant_state_same_packet_subset P ->
refined_raft_net_invariant_reboot' P ->
refined_raft_intermediate_reachable net ->
P net.