Lemma handleMessage_applied_entries : forall net h h' 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) -> applied_entries (nwState net) = applied_entries (update name_eq_dec (nwState net) h st').