Lemma handleMessage_log : forall net h h' h'' e m st' ms, raft_intermediate_reachable net -> In {| pBody := m; pDst := h; pSrc := h' |} (nwPackets net) -> handleMessage h' h m (nwState net h) = (st', ms) -> In e (log (update name_eq_dec (nwState net) h st' h'')) -> applied_implies_input_state (eClient e) (eId e) (eInput e) net.