Definition raft_net_invariant_client_request' (P : network -> Prop) :=
    forall h net st' ps' out d l client id c,
      handleClientRequest h (nwState net h) client id c = (out, d, l) ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      (forall h', st' h' = update name_eq_dec (nwState net) h d h') ->
      (forall p', In p' ps' -> In p' (nwPackets net) \/
                         In p' (send_packets h l)) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_timeout' (P : network -> Prop) :=
    forall net h st' ps' out d l,
      handleTimeout h (nwState net h) = (out, d, l) ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      (forall h', st' h' = update name_eq_dec (nwState net) h d h') ->
      (forall p', In p' ps' -> In p' (nwPackets net) \/
                               In p' (send_packets h l)) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_append_entries' (P : network -> Prop) :=
    forall xs p ys net st' ps' d m t n pli plt es ci,
      handleAppendEntries (pDst p) (nwState net (pDst p)) t n pli plt es ci = (d, m) ->
      pBody p = AppendEntries t n pli plt es ci ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) d h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         p' = mkPacket (pDst p) (pSrc p) m) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_append_entries_reply' (P : network -> Prop) :=
    forall xs p ys net st' ps' d m t es res,
      handleAppendEntriesReply (pDst p) (nwState net (pDst p)) (pSrc p) t es res = (d, m) ->
      pBody p = AppendEntriesReply t es res ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) d h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         In p' (send_packets (pDst p) m)) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_request_vote' (P : network -> Prop) :=
    forall xs p ys net st' ps' d m t cid lli llt,
      handleRequestVote (pDst p) (nwState net (pDst p)) t (pSrc p) lli llt  = (d, m) ->
      pBody p = RequestVote t cid lli llt ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) d h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         p' = mkPacket (pDst p) (pSrc p) m) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_request_vote_reply' (P : network -> Prop) :=
    forall xs p ys net st' ps' d t v,
      handleRequestVoteReply (pDst p) (nwState net (pDst p)) (pSrc p) t v = d ->
      pBody p = RequestVoteReply t v ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) d h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys)) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_do_leader' (P : network -> Prop) :=
    forall net st' ps' d h os d' ms,
      doLeader d h = (os, d', ms) ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      nwState net h = d ->
      (forall h', st' h' = update name_eq_dec (nwState net) h d' h') ->
      (forall p, In p ps' -> In p (nwPackets net) \/
                             In p (send_packets h ms)) ->
      P (mkNetwork ps' st').Definition raft_net_invariant_do_generic_server' (P : network -> Prop) :=
    forall net st' ps' d os d' ms h,
      doGenericServer h d = (os, d', ms) ->
      P net ->
      raft_intermediate_reachable net ->
      raft_intermediate_reachable (mkNetwork ps' st') ->
      nwState net h = d ->
      (forall h', st' h' = update name_eq_dec (nwState net) h d' h') ->
      (forall p, In p ps' -> In p (nwPackets net) \/
                             In p (send_packets h ms)) ->
      P (mkNetwork ps' st').

(* Specifications: *)
Lemma raft_invariant_handle_message' P : forall xs p ys net st' ps' d l, raft_net_invariant_append_entries' P -> raft_net_invariant_append_entries_reply' P -> raft_net_invariant_request_vote' P -> raft_net_invariant_request_vote_reply' P -> handleMessage (pSrc p) (pDst p) (pBody p) (nwState net (pDst p)) = (d, l) -> P net -> raft_intermediate_reachable net -> raft_intermediate_reachable (mkNetwork ps' st') -> nwPackets net = xs ++ p :: ys -> (forall h, st' h = update name_eq_dec (nwState net) (pDst p) d h) -> (forall p', In p' ps' -> In p' (xs ++ ys) \/ In p' (send_packets (pDst p) l)) -> P (mkNetwork ps' st').
Lemma raft_invariant_handle_input' P : forall h inp net st' ps' out d l, raft_net_invariant_timeout' P -> raft_net_invariant_client_request' P -> handleInput h inp (nwState net h) = (out, d, l) -> P net -> raft_intermediate_reachable net -> raft_intermediate_reachable (mkNetwork ps' st') -> (forall h', st' h' = update name_eq_dec (nwState net) h d h') -> (forall p', In p' ps' -> In p' (nwPackets net) \/ In p' (send_packets h l)) -> P (mkNetwork ps' st').