Definition write_ghost_log (h : name) (st : @data raft_refined_base_params) : ghost_log := log (snd st).Definition raft_msg_refined_base_params := mgv_refined_base_params.Definition raft_msg_refined_multi_params := mgv_refined_multi_params.Definition raft_msg_refined_failure_params := mgv_refined_failure_params.Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Inductive msg_refined_raft_intermediate_reachable : network -> Prop :=
  | MRRIR_init : msg_refined_raft_intermediate_reachable step_async_init
  | MRRIR_step_failure :
      forall failed net failed' net' out,
        msg_refined_raft_intermediate_reachable net ->
        step_failure (failed, net) (failed', net') out ->
        msg_refined_raft_intermediate_reachable net'
  | MRRIR_handleInput :
      forall net h inp gd out d l ps' st',
        msg_refined_raft_intermediate_reachable net ->
        handleInput h inp (snd (nwState net h)) = (out, d, l) ->
        update_elections_data_input h inp (nwState net h) = gd ->
        (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 (add_ghost_msg h (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_handleMessage :
      forall p net xs ys st' ps' gd d l,
        msg_refined_raft_intermediate_reachable net ->
        handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
        update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
        nwPackets net = xs ++ p :: ys ->
        (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
        (forall p', In p' ps' -> In p' (xs ++ ys) \/
                           In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doLeader :
      forall net st' ps' h os gd d d' ms,
        msg_refined_raft_intermediate_reachable net ->
        doLeader d h = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st')
  | MRRIR_doGenericServer :
      forall net st' ps' os gd d d' ms h,
        msg_refined_raft_intermediate_reachable net ->
        doGenericServer h d = (os, d', ms) ->
        nwState net h = (gd, d) ->
        (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 (add_ghost_msg h (gd, d') ms))) ->
        msg_refined_raft_intermediate_reachable (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_client_request (P : network -> Prop) :=
    forall h net st' ps' gd out d l client id c,
      handleClientRequest h (snd (nwState net h)) client id c = (out, d, l) ->
      gd = update_elections_data_client_request h (nwState net h) client id c ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      (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 (add_ghost_msg h (gd, d) l))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_timeout (P : network -> Prop) :=
    forall net h st' ps' gd out d l,
      handleTimeout h (snd (nwState net h)) = (out, d, l) ->
      gd = update_elections_data_timeout h (nwState net h) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      (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 (add_ghost_msg h (gd, d) l))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_append_entries (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d m t n pli plt es ci,
      handleAppendEntries (pDst p) (snd (nwState net (pDst p))) t n pli plt es ci = (d, m) ->
      gd = update_elections_data_appendEntries (pDst p) (nwState net (pDst p)) t n pli plt es ci ->
      snd (pBody p) = AppendEntries t n pli plt es ci ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         p' = mkPacket (pDst p) (pSrc p) (write_ghost_log (pDst p) (gd, d), m)) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_append_entries_reply (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d m t es res,
      handleAppendEntriesReply (pDst p) (snd (nwState net (pDst p))) (pSrc p) t es res = (d, m) ->
      gd = (fst (nwState net (pDst p))) ->
      snd (pBody p) = AppendEntriesReply t es res ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) m))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_request_vote (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d m t cid lli llt,
      handleRequestVote (pDst p) (snd (nwState net (pDst p))) t (pSrc p) lli llt  = (d, m) ->
      gd = update_elections_data_requestVote (pDst p) (pSrc p) t (pSrc p) lli llt (nwState net (pDst p)) ->
      snd (pBody p) = RequestVote t cid lli llt ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         p' = mkPacket (pDst p) (pSrc p) (write_ghost_log (pDst p) (gd, d), m)) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_request_vote_reply (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d t v,
      handleRequestVoteReply (pDst p) (snd (nwState net (pDst p))) (pSrc p) t v = d ->
      gd = update_elections_data_requestVoteReply (pDst p) (pSrc p) t v (nwState net (pDst p)) ->
      snd (pBody p) = RequestVoteReply t v ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys)) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_do_leader (P : network -> Prop) :=
    forall net st' ps' gd d h os d' ms,
      doLeader d h = (os, d', ms) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwState net h = (gd, d) ->
      (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 (add_ghost_msg h (gd, d') ms))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_do_generic_server (P : network -> Prop) :=
    forall net st' ps' gd d os d' ms h,
      doGenericServer h d = (os, d', ms) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwState net h = (gd, d) ->
      (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 (add_ghost_msg h (gd, d') ms))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_state_same_packet_subset (P : network -> Prop) :=
    forall net net',
      (forall h, nwState net h = nwState net' h) ->
      (forall p, In p (nwPackets net') -> In p (nwPackets net)) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      P net'.Definition msg_refined_raft_net_invariant_reboot (P : network -> Prop) :=
    forall net net' gd d h d',
      reboot d = d' ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      nwState net h = (gd, d) ->
      (forall h', nwState net' h' = update name_eq_dec (nwState net) h (gd, d') h') ->
      nwPackets net = nwPackets net' ->
      P net'.Definition msg_refined_raft_net_invariant_init (P : network -> Prop) :=
    P step_async_init.Definition msg_refined_raft_net_invariant_client_request' (P : network -> Prop) :=
    forall h net st' ps' gd out d l client id c,
      handleClientRequest h (snd (nwState net h)) client id c = (out, d, l) ->
      gd = update_elections_data_client_request h (nwState net h) client id c ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_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 (add_ghost_msg h (gd, d) l))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_timeout' (P : network -> Prop) :=
    forall net h st' ps' gd out d l,
      handleTimeout h (snd (nwState net h)) = (out, d, l) ->
      gd = update_elections_data_timeout h (nwState net h) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_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 (add_ghost_msg h (gd, d) l))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_append_entries' (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d m t n pli plt es ci,
      handleAppendEntries (pDst p) (snd (nwState net (pDst p))) t n pli plt es ci = (d, m) ->
      gd = update_elections_data_appendEntries (pDst p) (nwState net (pDst p)) t n pli plt es ci ->
      snd (pBody p) = AppendEntries t n pli plt es ci ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         p' = mkPacket (pDst p) (pSrc p) (write_ghost_log (pDst p) (gd, d), m)) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_append_entries_reply' (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d m t es res,
      handleAppendEntriesReply (pDst p) (snd (nwState net (pDst p))) (pSrc p) t es res = (d, m) ->
      gd = (fst (nwState net (pDst p))) ->
      snd (pBody p) = AppendEntriesReply t es res ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) m))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_request_vote' (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d m t cid lli llt,
      handleRequestVote (pDst p) (snd (nwState net (pDst p))) t (pSrc p) lli llt  = (d, m) ->
      gd = update_elections_data_requestVote (pDst p) (pSrc p) t (pSrc p) lli llt (nwState net (pDst p)) ->
      snd (pBody p) = RequestVote t cid lli llt ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys) \/
                         p' = mkPacket (pDst p) (pSrc p) (write_ghost_log (pDst p) (gd, d), m)) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_request_vote_reply' (P : network -> Prop) :=
    forall xs p ys net st' ps' gd d t v,
      handleRequestVoteReply (pDst p) (snd (nwState net (pDst p))) (pSrc p) t v = d ->
      gd = update_elections_data_requestVoteReply (pDst p) (pSrc p) t v (nwState net (pDst p)) ->
      snd (pBody p) = RequestVoteReply t v ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
      nwPackets net = xs ++ p :: ys ->
      (forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
      (forall p', In p' ps' -> In p' (xs ++ ys)) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_do_leader' (P : network -> Prop) :=
    forall net st' ps' gd d h os d' ms,
      doLeader d h = (os, d', ms) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
      nwState net h = (gd, d) ->
      (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 (add_ghost_msg h (gd, d') ms))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_do_generic_server' (P : network -> Prop) :=
    forall net st' ps' gd d os d' ms h,
      doGenericServer h d = (os, d', ms) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
      nwState net h = (gd, d) ->
      (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 (add_ghost_msg h (gd, d') ms))) ->
      P (mkNetwork ps' st').Definition msg_refined_raft_net_invariant_state_same_packet_subset' (P : network -> Prop) :=
    forall net net',
      (forall h, nwState net h = nwState net' h) ->
      (forall p, In p (nwPackets net') -> In p (nwPackets net)) ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      P net'.Definition msg_refined_raft_net_invariant_reboot' (P : network -> Prop) :=
    forall net net' gd d h d',
      reboot d = d' ->
      P net ->
      msg_refined_raft_intermediate_reachable net ->
      msg_refined_raft_intermediate_reachable net' ->
      nwState net h = (gd, d) ->
      (forall h', nwState net' h' = update name_eq_dec (nwState net) h (gd, d') h') ->
      nwPackets net = nwPackets net' ->
      P net'.

Lemma msg_refined_raft_net_invariant_append_entries_reply'_weak : forall net, msg_refined_raft_net_invariant_append_entries_reply net -> msg_refined_raft_net_invariant_append_entries_reply' net.