SSL Aodv.thy

(*  Title:       Aodv.thy
    License:     BSD 2-2-Clause See LICENSE.
    Author:      Timothy Bourke, Inria
*)

section The AODV protocol" Aodv

theoryAWN.AWNAWN_SOSabels AWN.N_Iariants
imports Aodv_Data Aodv_Message
        AWN.AWN_SOS_Labels AWN.AWN_Invariants
begin "state statejava.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14

subsection "Data state"

record state =
  ipome_neq_not_eq<>(
  sn    :: java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
  rt    : rt
  rreqs :: "(ip \<timesdests= (SOME x. True),
  rreqid := (SOME x. True),
  (* all locals *)
  msg :: "msg    =SOME. True)java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
  data"ata"
  dests  :: "ip ⇀
  pre :: "ip"
  rreqid ""
  dip :: "ip    :=(OME ≠ ξ"
  oip : ""
  hops :: "nat clear_locals_def
  dsn "sqn"
  dsk    :: "k"
  osn
  sipip

abbreviation aodv_init :: "ip ==> state"
where< <java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
         ip = i,
         sn = 1,
         rt = Map.empty,
         rreqs = {},
         store = Map.empty,

         msg    = (SOME x. True),
         data   = (SOME x. True),
         dests  = (SOME x. True),
         pre    = (SOME ),
         rreqid
         dipcals_def
         oip
         hops   ( x. True
          is_newpkt
         dsk " ξ case msg ξ
         osn = (SOME x. True),
         sip = S x. x ≠
       )

lemma some_neq_not_eq [simp]: "¬
  bysome_eq_exumeral

definition clear_locals''p <>{ <><
where "clear_locals ξ = ξ (
    msg := (SOME x. True),
    data := (SOME x. True),
    is_rreq ξ case msg ξ
    pre := (SOME x. True),
    rreqid := (SOME x. True),
    dip := (SOME x. True),
    oip = (SOME x.Tru),
    hops := (SOME x. True),{ <>\lparr h := hops', rreqid := rreqid', dip :=di', dsn := dsn',
    dsn := (SOME x.T),
    dsk := (SOME x. T _ ==>
    osn := (SOME x. True),
    sip := (SOME x. x ≠'n' dip' dsn' dsk' oip osn' sip'.
  )<' = ξ(

lemmap [simp]: "¬(sip) = ip ξ
  unfolding  using  unfoldingis_rreq_def

lemma clear_locals_but_not_globals
  "ip (clear_locals ξ
  "ls) = sn ξ
  java.lang.NullPointerException: Cannot invoke "String.equals(Object)" because "brackoff" is null
  "rreqs (clear_locals java.lang.NullPointerException
  "tore(lear_lols \xi>) = store \xi>"
  unfolding clear_locals_def by is_rerr>≡ of

subsection "Auxilliary message Rerr dests' sip ==>(' )

definition is_newpkt
where "is_newpkt
                        is_rerr_asm!
                     | _ ==>

definition is_pkt
where "is_pkt ξ msg \xi rrdet sp'\>
                     ξ\<<rparr
                  |_ ==> {}"

definition is_rreq
where "is_rreq ξ ≡ case msg ξ of
                     Rreq hops' rreqid' dip' dsn' dsk' oip' osn' sip' ==>
                       { ξ( hops := hops', rreqid := rreqid'di:= dip dsn := dsn'
                            dsk := dsk', oip := oip', osn := osn', sip lemmas i is_msg_dfs =
                   | _ ==> {}"

lemmais_rreq_asm!
  assumes "ξ' ∈' ∈ ξ ip ξ' = ip ξ"
    "(\existsh' reqid'dip' sn'dsk'oip osn sip'
               msg ξ"<>    ==>' = ip \xi"
               ξ( hops := hops', rreqid := rreqid', dip := dip', dsn := dsn',
                       dsk := dsk', oip := oip', osn := osn', sip := sip' ) "ξ is_newpkt ξ ==>' = ip ξ
  using assms unfolding is_rreq_def (cases "msg ξ
  by (cases "msg

definitionp
where "is_rrep ξ' ∈ ==>' = sn ξ
                     Rrep hops' dip' dsn' oip' sip' ==>
                       { ""i is_rreq ξ ==><>' = sn \xi>"
                   | _ ==>

lemma is_rrep_asm
  assumescases ξ
    shows "(∃ is_msg_in [sim]:
               msg ξ = Rrep hops' dip' dsn' oip' sip' ∧
               ξ' = ξ hops := hops', dip := dip', dsn := dsn', oip := oip', sip := sip' )
  using assms unfolding is_rrep_def
  by (cases "msg") simp_all

definition is_rerr
where "is_rerr <xi  case msg ξ of
                     Rerr dests sip { ξ( }
                   | _ ==> {}"

lemma is_rerr_asm [dest!]:
  assumes "ξ' ∈]
    shows "(∃
                msg ξ = Rerr dests' sip' ∧
               ξ' = ξ( dests := dests', sip := sip' ))"
  using assms unfolding is_rerr_def
  by (cases ""msg ξ") simp_all

lemmas is_msg_defs =
  is_rerr_def is_rrep_def is_rreq_def is_pkt_def is_nis_nekt_

lemma is_msg_inv_ip [simp]:
  "ξ' ∈ is_rerr ξ   ==> ip ξ' = ip ξ"
  "ξ' ∈ is_rrep ξ   ==> ip ξ' = ip ξ"
  "ξ' ∈ is_rreq ξ   ==> ip ξ' = ip ξ' ∈ ==>' "
  "<xi 
  "ξ nis_newpkt ξLongrghtarrow> ip ξ' = ip ξ"
  unfolding is_msg_defs
  by (cases "msg ξ", clarsimp+)+

lemma is_msg_inv_sn [simp]:
  "ξ' ∈ is_rerr ξ ==> sn ξ= sn ξ
  "ξ' ∈ is_rrep ξ   ξ is_rrep ξ   ==> ξ<xi"
  ""\xi>' ∈<xi> ==> store ξ ξ
  "ξ' ∈    ==> sn ξ' = sn ξ"
  "ξ is_newpkt ξ ==>' = sn ξ
  unfolding is_msg_defs
  by (casesmsg", clarsimp+)+

lemma is_msg_inv_rt [simp]:
  "ξ is_rerr ξ   ==>>' = rt ξ
  "ξ' ∈
  "ξ' ∈' ∈    ==>' = sip\xi"
  "ξ' ∈ is_pkt ξ    ==> rt ξ' = rt ξ"
  "ξ"ξ ξ sip ξ' = sip ξ
  unfolding is_msg_defs
  by (cases "msg ξ", clarunfoldis_ms_

lemma is_msg_inv_rreqs [simp]:
  "ξ' ∈
  "ξ' ∈
  "ξ' ∈ is_rreq ξ   ==> rreqs ξ' = rreqs ξ"
  "ξ' ∈ is_pkt ξ    ==> rreqs ξ' = rreqs ξ"
   PRer
  unfolding is_msg_defs
  by (cases "msg ξ:: "pseqp <Rightarro

lemma is_
  "ξ' ∈ is_rerr ξ   ==> store ξ' = store ξ"
  "ξ' ∈ is_rrep ξ   ==> store ξ' = store ξ"
  "\xi>' \in> s_rreq ξ store ξ' = store<>
  "ξ P = 2"
  \xi'\in>  ξ store ξ =store"
  unfolding is_msg_defs
  by (cases "msg ξ", clarsim naPRrep = 5""

lemma is_msg_inv_sip [simp]:
  "ξ ∈    ==>' = sip ξ
  "ξ
  unfolding is_msg
  by (cases "msg

subsection "The protocol process"

datatype pseqp =
    PAodv
  | PNewPkt
  | PPkt
  | PRreq
  |
  | PRerr

fun nat_of_seqp ::"pseqp <Right nat"
where
  "nat_of_seqp PAodv = 1"
| "nat_of_seqp PPkt = 2"
| "nat_of_seqp PNewkt = 3"
| "nat_of_seqp PRreq = 4"
| "nat_of_seqp PRrep = 5"
| "nat_of_seqp PRerr = 6"

instantiation "pseqp" :: ord
begin
definition less_eq_seqp [iff]: "l1 ≤ l2 = (nat_of_seqp l1 ≤ nat_of_seqp l2)"
definition less_seqp [iff]:    "l1 < l2 = (nat_of_seqp l1 < nat_of_seqp l2)"
instance ..
end

abbreviation AODV
where
  "AODV ≡ λ_. [clear_locals] call(PAodv)"

abbreviationPKT
where
  "PKT args ≡

     , di, oip)= = args\<xi 
         (clear_locals ξ)"
     kt
abbreviation NEWPKT
where
  "NEWPKT args ≡
     [. let (data, dip) = args ξ
         (clear_locals ξ) (<lbrakk>ξ(data, didip) = args ξ
     call(PNewPkt)"

abbreviation RREQ
where
  "RREQ args ≡
     [. let (hops, rreqid, dip, dsn, dsk, oip, osn, sip = args \xii
         (clear_locals ξ args ≡
                            dsn := dsn dsk := d, oip := oip,
                            osn := osn, sip := sip )
     call(PRreq)"

abbreviation RREP
where
  "RREP arg args ≡
     [. let (hops, dip, dsn, oip, sip) = = a ξ
         (clear_locals ξ
                            oip := oip, sip := sip )
     call(PRrep)"

abbreviation RERR
where
  "RERR args ≡
     [) (n,
         (clear_locals ξ ( dests := dests, sip := sip )]
     call(PRerr)"

fun Γjava.lang.NullPointerException
where
  java.lang.NullPointerException
     receive(λmsg' ξ. ξξ. let (dests, sip) = arg \xi in
     ( (clear_locas \<xi  \\rp>\rbrakk
       ⊕ callPRer)"
       ⊕_O<^sub_V :: "(state, msg, pseqp, pseqp label) seqp_env"
            [_OV PAodv = labelled PAodv (
            RREQ(λ     receive(λ \xi> \xi <lparr := msgrparr.
       ⊕ ⟨⟩
            [ξ. ξ ( (rt ξ \xi> (, unk, val 1 sip \xi, })\rparr><>
            RREP(λξ ξξξ, sip ξ
       ⊕ ⟨rangle
            [xi> () (sip ξ , 1,sip, {}) )
            RERR(λ(λ. (hops <xi,, dip>, dsn ξ, oip ξ, sip ξ
     )
     ⊕ξ( ) qD(store ξ) <> 
          [ξ. ξ ( data := hd(σξ. ξ ( (rt ξ ξ(0, unk, val, 1, sip ξ, {}) )]
          unicastξ (rt) (dip ξξ, dip ξ\xi>))
            [. ξ store := the (drop (dip ξxi)) )
            AODV()
          ▹ξ. <xi  dests := (λrip. if ∈) ∧) rip = nhop ( ξ>))
                                      (incsqnrt) rip)) else) )
             [ ⟨ξ( | dip. dip ∈) ∩) }\rangle>
             [. ξ store := setRRF (store ξ]
             [ξ. ξ ( pre := ∪ξ (nhop \xi)( ξξ < dip ξ)).
             [<xilparr dests := (λ. ifdests) rip ≠∧the(precs ξ<>{)
                                     then()
             groupcast(λξ ξξrerr(dests, ip ξ) AODV()
     ⊕ ⟨then Some (inc (sqn ξelse) )
             | dip. dip ∈ 🚫
         \>ξ. ξ ( store := unsetRRF (store ξ) (dip ξ) )]
         [ξ. ξ ( sn : incsni]
         [ξ. ξ ( rreqid[. ξ dests := (<lambda. ifdests ξ None ∧ theprecs (rtxi) rip) noteq{})
         <lbrakk                    ) rip else None)rparr
         broadcast(λξ. rreq(0, rreqid ξ, dip ξ, sqn (rt ξ) (dip ξ(λ<xipre ξ, λξ. rerr(dests, ip ξ()
                            ip<xi>, sn \>, ip)). AODV()"

| "Γ_\xi. <> ( store ξ) )
     ⟨\i. ξ ( ξ]
        deliver(λ).AODV()
     ⊕ξξ (  := rreqs ∪, rreqid)} )
        \lbrakk>ξ ( ξ) (store ξ]
        AODV ξ, ip ξ)"

| "Γ_OV PNewPkt = labelled PNewPkt (
     <>\
        deliver(λξdip< =
     < ⟨  <xi  ip⟩
     (
       <\<)dip) (store) \rparrjava.lang.StringIndexOutOfBoundsException: Index 108 out of bounds for length 108
         unicastξ ξ)), λ. pkt(data, dip ξ
         ▹
           [. <> <>dests= (<>. if ∈) ∧) rip (rt) (dip ξ
                                   then Some (inc (sqn (rt 
           ξ. ξ rt := invalidate (rt ξxi )]
           [ξ. ξ (  (rtxi (dip ξ)), λξ. pkt(data ξ, dip ξ \xi>)AODV(java.lang.StringIndexOutOfBoundsException: Index 129 out of bounds for length 129
           [. ξ\lparr  := ∪) rip) | rip. rip ∈ ξ]
           [ξ. ξ ( dests := (λrip. if ((dests ξ) ripthenSome (incsqn <>) rip None]
                                   then<)  else]
           groupcast<xi. ξ,ip)).AODV
       ⊕\ pre :\{ the (precs rt) rip |. rip dom (dests ξ]
       (
           ⟨ξ. dip ξ ∈ iD (rt<)⟩
             groupcastξ (rt) (dip ξ
                       λξ. rerr([dip ξ ↦ sqn (rt ξ) (dip(<lambda\. pre, λ. rerr(dests\xi  ξ
           <oplus\ ξ iD (rt ξ)⟩
              AODV()
       )
     ))"

| "Γ_\xi (precs (rt\xi>)( ξ
     ⟨oip, rreqid <xi) rreqs ξ
       AODV()
     ⊕ξ, rreqid ξ rreqs ξ⟩
       [ ( (rt <xi)) (osn <>,
       [
       (
         ⟨subA_Djava.lang.NullPointerException
           ξ () (dsn ξ]
           unicast(λ
           ▹
             [. ξ dests := (λ ∈) \and nhop <>))rip (rt) (oip ξ
                                     then Some inc) rip)  java.lang.StringIndexOutOfBoundsException: Index 102 out of bounds for length 102
             \lbrakk><>.]
             <lbrakk :=setRRF) (dests <xi)]
             \>
             ξ (rip ((dests) rip ≠ the(precsrt) rip) ≠
                                     then (dests ξ[.ξ dests := (λ vD (rt ξ nhop (rt ξ nhop(rt) (oip ξ
             (λ. preξξ ξ)).AODV()
         ⊕. ξ rt := invalidate (rt) (dests <xi)]
         (
           ⟨ξξ () (dests ξ]
             [. ξ rt := the (addpreRT ξ) {sip ξ]
             [ ( (rt ξ ξ (rt) (dip ξ]
             unicast                  (destsxi>) ) rip else) )
                         sqn ξ), oipξ
             AODV()
           ▹          langle<xi>. dip ξ ∈ vD (rt ξ> dsn ξ ≤) (dip) ∧) (dip) = knojava.lang.StringIndexOutOfBoundsException: Index 156 out of bounds for length 156
             \lbrakk\xi>. ξ dests := (<>. if ∈) ∧) rip =nhop ξ))
                                     then Some (sqn ξNone]
             <lbrakk\ <> rt=invalidate <>)
             [
             [ξ (rip ∈ nhop (rt) rip  ( ξ))
             <>\rip (( ξ None ∧ (rt<xi) rip) ≠
                                     then (dests\lbrakk<xi>. ξ (invalidatert \xi) (dests ξ]
             groupcast(<lambda\. rerr ξ)).AODV()
           ⊕ξ <lparr> pre <Union>{ the (precs (rt ξ) rip) | rip. rip ∈ ξ]
             broadcast(λ<lbrakkxi. ξ dests := (λrip. if (( ξ <> ) ) ≠
                                 \, oip <>,
             ()
         )
       ))"

| "Γ, oip, osn <> ip\>)).
     ⟨
     (
       [
       (
         ⟨ξ oip\xi =  ξ
            AODV()
         java.lang.NullPointerException: Cannot invoke "String.equals(Object)" because "brackoff" is null
         (
           \langle>ξ. oip ξ ∈ vD (rt ξ
             [ξ. ξ AODV)
             [ξ. ξ( (rt\xi> (the(nhop ξ ξ
                                               {the (nhop (rt ξ) (oip ξξ. ξ> dests := (λrip (rip vD (rt ξ) <> nhop ξ (rt<i)(oip ξ))
             unicast(λξ. the (nhop                                      then (inc (sqnrt) rip)) else None) )
             AODV
           ▹. ξ store := setRRF (store ξ) (dests ξ))
             [xi ( := (λ.ifrip> vD (rt ξ) ∧ (rt ξ  nhop (rt ξ ξ
                                     then Some (inc (sqn[. ξ dests := (λripif (( ξ <>None <>  {})
             [ rt = (rt) (destsxi>) )
             [ (store ξ <xi)
             [ξ ⟨<xi. ∉)⟩
             [
                                     
             groupcast(λ. pre<, λ. rerr(dests>, ip ξ
           ⊕
             AODV()
         )
       )
     )
     ⊕ <Rightarrow rip vD (rt \<xi>) \<and> he (t\xi)rip) =sipxi
         AODV()
     )"

|"<><^>A<subO<sub>\<subVPRerr= labelledPRerr (
\<lbrakk\<>.\<xi <lparr  : (<>rip.casedests \\>) rip of None \<> None
     <lbrakk\xi> <xi>\lparr pre <>{ the(precs(rt\xi)rip || rip.  \<> dom (destsxi> } \rparr\rbrakk
                                       > ( \<) rip <  thenSome rsn else ) \><>
     \lbrakk\xi. <xi>\<> rt : invalidate ( <> dests \<> <><brakk>
     groupcast>xi.pre<> <>\xi. ( <> ip\<>).AODV()"
     \<lbrakk>\<declare<><sub\^subO\<subD<subV. simpdel
\><> <> \<lparr> dests(<lambda>rip  ((dests \xi) rip <>None\<nd the precs(rt\> ) \noteq{}
                             then
     groupcast\<lambda><xi>.pre\<>,\lambda\xi. rerrdestsxi, \xi>). AODV))java.lang.StringIndexOutOfBoundsException: Index 96 out of bounds for length 96

declare \<Gamma>\<^sub>A\<^sub>O\<^sub|\Gamma><subA<subO\^subD<sub>  =seqp_skeleton (<><^subA<^subO<^>D\^sub> PNewPkt"

lemmas<>^A<^>\^>\^>     \GammaAsub<subD<> PRreq)

\><sub\<sub><>\^
where
    "\<Gamma>\<^sub>A\<^sub>O\| \<amma><subA<subO<^>D<subV_skeletonPRerr    seqp_skeleton(\Gamma>\^>\^>\^>D<subVPRerr)"
  | "\<Gamma>\<^sub>A \<Gamma\^>A\<subO<subD<subV_skeleton_wf[simp]:
| "\>\<^sub>A\^sub>\^>\^subV_skeletonPPkt= seqp_skeleton (<>\<sub>\^>O\<subD<subVPPkt)"
  | "\<Gamma>\<^sub>A\<^sub>O\<^sub>Dproof (,  allI
  | \Gamma\<sub\^ubO\^sub>\^>V_skeletonPRrep    seqp_skeleton ((<><subA<><>\^>VPRrep)java.lang.StringIndexOutOfBoundsException: Index 128 out of bounds for length 128
  | "\<Gammajava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 5

lemma \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V_skeleton_wf [simp]:
  "wellformed \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V_skeleton"
  proof (rule, intro allI)
    fix pn pn'
    show "call(pn') \<notin> stermsl (\<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V_skeleton pn)"
      by (cases pn) simp_all
  qed

declare \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<lemmas<>\<subA\^>O<subD<^subV_skeleton_simps simp code  \Gamma\^>\^ubO\^subD<^>V_skeletonsimps[implified\Gamma>\^>A\^>\^>D<subV_simps seqp_skeleton.imps]

lemmas \fixes p pn

lemma aodv_proc_cases [dest](p \in>  (\Gamma\^sub>\^>\<^>D\subVPAodv) \or
  fixes p pn
   p \in  <><^>\subO\^sub><subVpn)\Longrightarrow
                                (p \<in> ctermsl (\                                  <> ctermsl(<Gamma><^>\^>\^>D<subVPPkt  \<or
                                 p \<in> ctermsl (\<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V PNewPkt)  \<or>
                                 p \<in> ctermsl (\<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V PPkt)  \<or>
                                 p \<in>ctermsl\<Gamma>^subA\<subO\sub
                                 p \<in\>^>\^>O\^>\^>V :"ip \Rightarrow state \times (java.lang.StringIndexOutOfBoundsException: Index 132 out of bounds for length 132
                                 
  by (cases:ip<>( times statemsg ,pseqp)seqp msgseq_action automaton

<\^>\^>\<sub\^> :ip\Rightarrow state<times (state msg,pseqp pseqp label seqp) set
where

abbreviationpaodv
  :: "java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
where
  "paodv i \<equiv> \<lparr> init = \<sigma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V i, trans = seqp_sos \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V \<rparr>"

lemma aodv_trans: "trans (paodv i) = seqp_sos \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V"
  by simp

lemma aodv_control_within [simp]: "control_within \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V (init java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  unfolding\<>\<sub\^subO\^>> by(rulecontrol_withinI auto : \<Gamma>\^subA\^subO\^subD<sub>_)

lemma aodv_wf [simp]:
  "wellformed \< call' <>stermsl (<\^>\^subO\^^sub )java.lang.StringIndexOutOfBoundsException: Index 83 out of bounds for length 83
  proof (rule,aodv_labels_not_empty simp =labels_not_empty [OF]
    fix pn pn'
showcall(pn)<>stermsl\Gamma<sub<subO^D<sub>Vpn
      by (cases pn) simp_all
  qed

lemmas aodv_labels_not_empty [simp] = labels_not_empty [OF aodv_wf]

lemma aodv_ex_label [intro]: "\<exists>l. l\<in>labels \<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V p"
  by (metis aodv_labels_not_empty all_not_in_conv)

lemma aodv_ex_labelE [elim]:
s\Gamma>subA<sub>\subD<subVp Plp"
      and shows"
     ""
  using java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

lemma aodv_simple_labels [simp]: "simple_labels \<Gamma>\<^sub>fix pn 
  proof
    fix pn p
    assume "p\<in>subterms(\<Gamma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V pn)"
     \exists!l labels <><subA<^>O\^>D\>Vp={}java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
    by ( pn( cong:seqp_congs |elim disjE)java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
  qed

>\^>\^> []: (<> )\in>\<>^>\^>\^>\^> i\Longrightarrowlabels<><sub\>\^>D<subVp=PAodv:}
  unfolding \<sigma   <>\<^>A<^>O\sub\^sub> byjava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64

lemma aodv_init_kD_empty [ <><sub\<^subO\^>D<subV_def kD_def  simp
  "(\<xi>, p) \<in> \<sigma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V aodv_init_sip_not_ip simp]:"\>sipaodv_init i = ) bysimp
  unfolding \<sigma>\<^sub>A\<^sub>O\<^sub>D\<^sub> aodv_init_sip_not_ip:

lemma aodv_init_sip_not_ip [simp]: "\<not>(sip (aodv_init i) = i)" by simp

lemma aodv_init_sip_not_ip' assmsunfolding<><subA<^subO<sub>D\^sub>V_defby simp
 (xi,p <>\<><sub^>sub\^sub java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
shows "sip \<xi> \<noteq> ip \<xi>"
  using assms unfolding \<sigma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V_def by simp

lemma aodv_init_sip_not_i [simp]:
  assumes "(\<xi>, p) \<in> \<sigma>\<^sub>A\<^sub>O\<^sub>D\<^sub>V i"
    shows "sip \<xi> \<noteq> i"
  using assms unfolding \<sigma>\<^sub>A\<^sub>O\<^sub>

lemma clear_locals_sip_not_ip':
  assumes "ip \<xi> = i"
    shows "<not> (clear_locals \<xi) i"
  using

text \openStopthe   descendingintoprocess terms\<lose>
declare seqp_congs [cong]

text \<open>Configure the main invariant tacticseq_invariant_ctermsI [OF aodv_wfaodv_control_withinaodv_simple_labels aodv_trans,

declare
  \<Gamma>\<^sub>A\<^sub>O\<^sub>  seq_step_invariant_ctermsI[OFaodv_wf aodv_simple_labelsaodv_trans
  aodv_proc_cases [ctermsl_cases]
  seq_invariant_ctermsI [OF aodv_wf aodv_control_within aodv_simple_labels aodv_trans,
                            cterms_intros]
  seq_step_invariant_ctermsI [OF aodv_wf aodv_control_within aodv_simple_labels aodv_trans,
                                 cterms_intros]

end