Proof using.
intros.
prep_induction H.
induction H using refl_trans_1n_trace_n1_ind; intros; subst.
- find_inversion. auto.
- destruct x'. simpl in *.
eapply RIR_step_failure; [|eauto].
eauto.
Qed.
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 ->
(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 ->
(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 ->
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 ->
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 ->
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 ->
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 ->
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 ->
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').

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 ->
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').