Lemma refined_raft_invariant_handle_input' P : forall h inp net st' ps' gd out d l, refined_raft_net_invariant_timeout' P -> refined_raft_net_invariant_client_request' P -> handleInput h inp (snd (nwState net h)) = (out, d, l) -> update_elections_data_input h inp (nwState net h) = gd -> P net -> refined_raft_intermediate_reachable net -> refined_raft_intermediate_reachable (mkNetwork ps' st') -> (forall h', st' h' = update name_eq_dec (nwState net) h (gd, d) h') -> (forall p', In p' ps' -> In p' (nwPackets net) \/ In p' (send_packets h l)) -> P (mkNetwork ps' st').