{ 
sth:SecurityTheory
(CRX-protocol{i:l}(sth-es(sth)) |= ... authenticates 2 messages
CRX-protocol{i:l}(sth-es(sth)) |= ... authenticates 3 messages ) }
{ Proof }
Definitions occuring in Statement :
CRX-protocol: CRX-protocol{i:l}(s),
CR-responder6: CR-responder6{i:l}(s),
CR-initiator4: CR-initiator4{i:l}(s),
authentication: prtcl |= bs authenticates n messages ,
sth-es: sth-es(s),
security-theory: SecurityTheory,
all: x:A. B[x],
and: P Q,
natural_number: $n
Definitions :
limited-type: LimitedType,
universe: Type,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
set: {x:A| B[x]} ,
atom: Atom$n,
dep-isect: Error :dep-isect,
record+: record+,
ses-decrypt: Decrypt,
ses-encrypt: Encrypt,
ses-verify: Verify,
ses-sign: Sign,
ses-rcv: Rcv,
ses-send: Send,
int: 
,
ses-new: New,
in-eclass: e 
X,
es-E: E,
natural_number: $n,
ses-D-private: ses-D-private(s),
ses-D-public: ses-D-public(s),
cand: A c B,
record-select: r.x,
infix_ap: x f y,
es-causl: (e < e'),
union: left + right,
or: P 
Q,
rev_implies: P 
Q,
iff: P 
Q,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
pi1: fst(t),
ses-key-rel: MatchingKeys(k1;k2),
ycomb: Y,
ses-flow: ses-flow(s;es;a;e1;e2),
void: Void,
false: False,
assert: 
b,
sym: Sym(T;x,y.E[x; y]),
ses-K: PropertyK,
ses-S: PropertyS,
ses-D: PropertyD,
ses-R: PropertyR,
ses-V: PropertyV,
ses-flow-axiom: PropertyF,
ses-nonce-disjoint: NoncesCiphersAndKeysDisjoint,
ses-disjoint: ActionsDisjoint,
ses-ordering': ses-ordering'(s),
ses-NR: PropertyNR,
ses-NU: PropertyNU,
guard: {T},
ses-axioms: SecurityAxioms,
CR-responder6: CR-responder6{i:l}(s),
member: t T,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
ses-info: Info,
event-ordering+: EO+(Info),
ses-honest: Honest(A),
Id: Id,
equal: s = t,
not: 
A,
apply: f a,
is-basic-seq: thr[A;B] |= bs,
ses-thread: Thread,
matching-conversation: MatchingConversation(n;thr1;thr2),
prop: 
,
security-theory: SecurityTheory,
CR-initiator4: CR-initiator4{i:l}(s),
CRX-protocol: CRX-protocol{i:l}(s),
authentication: prtcl |= bs authenticates n messages ,
all: x:A. B[x],
implies: P Q,
function: x:A 
B[x],
exists: 
x:A. B[x],
and: P Q,
product: x:A 
B[x],
ses-thread-loc: loc(thr)= A,
sth-es: sth-es(s),
sq_type: SQType(T),
nil: [],
id-sdata: data(x),
pair: <a, b>,
sdata-pair: <d1, d2>,
atom-sdata: data(a),
token: "$token",
mk-pa: n(v),
cons: [car / cdr],
ses-is-protocol-action: pa(e),
minus: -n,
lelt: i j < k,
real: 
,
rationals: 
,
ses-act: Act,
subtype: S T,
add: n + m,
select: l[i],
lambda: 
x.A[x],
length: ||as||,
subtract: n - m,
true: True,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
lg-edge: lg-edge(g;a;b),
ses-action: Action(e),
ses-legal-sequence: Legal(pas) given prvt,
decidable: Dec(P),
int_seg: {i..j
},
event_ordering: EO,
es-locl: (e <loc e'),
so_lambda: 
x.t[x],
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
valueall-type: valueall-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
squash: 
T,
sq_stable: SqStable(P),
list: type List,
ses-protocol1-legal: Legal(bss),
ses-is-protocol-actions: pas(thr),
l_exists: (xL. P[x]),
ses-basic-sequence1: Basic1,
ses-protocol1-thread: (thr is one of bss at A),
ses-thread-member: e thr,
ses-protocol1: Protocol1(bss),
es-loc: loc(e),
ses-signer: signer(e),
es-base-E: es-base-E(es),
security-event-structure: SES,
encryption-key: Key,
event-has*: e has* a,
CR-responder5: CR-responder5{i:l}(s),
CR-responder4: CR-responder4{i:l}(s),
CR-initiator2: CR-initiator2{i:l}(s),
CR-initiator1: CR-initiator1{i:l}(s),
bool: 
,
atom: Atom,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
l_member: (x l),
l_all: (xL.P[x]),
l_contains: A B,
ses-legal-thread: Legal(thr)@A,
tl: tl(l),
hd: hd(l),
quotient: x,y:A//B[x; y],
bag: bag(T),
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
top: Top,
eclass-val: X(e),
sdata: SecurityData,
es-E-interface: E(X),
sqequal: s ~ t,
nat_plus: 
,
nat: ,
reducible: reducible(a),
prime: prime(a),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
dstype: dstype(TypeNames; d; a),
fset-member: a s,
f-subset: xs ys,
fset: FSet{T},
fset-closed: (s closed under fs),
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
consensus-rcv: consensus-rcv(V;A),
runEvents: runEvents(r),
pi2: snd(t),
btrue: tt,
record: record(x.T[x]),
sdata_atoms_pair: sdata_atoms_pair{sdata_atoms_pair_compseq_tag_def:o}(d2; d1),
null: null(as),
sdata_atoms_atom: sdata_atoms_atom{sdata_atoms_atom_compseq_tag_def:o}(a),
free-from-atom: x:T||a,
class-value-has: X(e) has a,
event-has: (e has a),
ses-info-flow: ->>,
rel_star: R^*,
release-before: (a released before e),
send-rcv-match: send-rcv-match(m1;m2),
spread: spread def,
lt_int: i <z j,
zip: zip(as;bs),
firstn: firstn(n;as),
ses-msg: isMsg(e),
thread-messages: thread-messages(thr),
tactic: Error :tactic,
iseg: l1 l2,
bEvents: Error :bEvents,
string: Error :string,
ses-encryption-key: key(e),
ses-decryption-key: key(e),
ses-private-key: PrivateKey(A),
tree: Tree(E),
rec: rec(x.A[x])
Lemmas :
atom1_sq,
atom_sq,
Id_sq,
guard_wf,
sdata_sq,
int_sq,
iseg_select2,
iseg_length,
iseg_same_length,
ses-thread-member_wf,
iseg_wf,
id-sdata-not-pair,
ses-msg-cases,
non_neg_length,
length_wf1,
l_all_cons,
and_functionality_wrt_iff,
l_all-nil,
l_all_wf2,
l_all_wf,
send-rcv-match_wf,
release-before_wf,
event-has*_wf,
ses-info-flow_wf,
rel_star_wf,
event-has_wf,
nonce-release-lemma2,
ses-protocol1-thread_wf,
nat_wf,
select_member,
es-loc_wf,
event-has*-iff,
class-value-has_wf,
sdata-has-atom,
cons_member,
id-sdata-one-one,
atom-sdata-one-one,
squash_wf,
bool_wf,
set_subtype_base,
eclass-val_wf,
ifthenelse_wf,
true_wf,
assert_elim,
pi1_wf_top,
pi2_wf,
sdata-pair-one-one,
atom-sdata_wf,
sdata-pair_wf,
id-sdata_wf,
id-sdata-not-pair2,
decidable__equal_int,
int_seg_properties,
es-interface-top,
sdata_wf,
ses-verify_wf,
subtype_rel_wf,
eclass_wf,
in-eclass_wf,
assert_wf,
top_wf,
es-interface-subtype_rel,
product_subtype_base,
sdata_subtype_base,
atom2_subtype_base,
atom1_subtype_base,
sq_stable__assert,
ses-sign_wf,
length_wf_nat,
es-interface-subtype_rel2,
es-base-E_wf,
subtype_rel_self,
ses-action_wf,
ses-new_wf,
ses-send_wf,
ses-rcv_wf,
ses-encrypt_wf,
encryption-key_wf,
ses-decrypt_wf,
ses-basic-sequence1_wf,
CR-initiator1_wf,
CR-initiator2_wf,
CR-responder4_wf,
CR-responder5_wf,
false_wf,
l_exists_wf,
iff_transitivity,
l_exists_cons,
or_functionality_wrt_iff,
iff_wf,
rev_implies_wf,
l_exists_nil,
l_member_wf,
le_wf,
int_subtype_base,
subtype_base_sq,
select_wf,
es-E_wf,
ses-act_wf,
member_wf,
es-locl_wf,
int_seg_wf,
event-ordering+_inc,
decidable__es-locl,
sq_stable_from_decidable,
sq_stable__all,
CRX-protocol-legal,
sth-es_wf,
not_wf,
Id_wf,
CRX-protocol_wf,
ses-thread_wf,
ses-thread-loc_wf,
is-basic-seq_wf,
CR-initiator4_wf,
matching-conversation_wf,
authentication_wf,
event-ordering+_wf,
ses-info_wf,
ses-honest_wf,
security-theory_wf,
CR-responder6_wf,
sth-axioms,
ses-axioms-imply,
ses-D-implies
\mforall{}sth:SecurityTheory
(CRX-protocol\{i:l\}(sth-es(sth)) |= CR-initiator4\{i:l\}(sth-es(sth)) authenticates 2 messages
\mwedge{} CRX-protocol\{i:l\}(sth-es(sth)) |= CR-responder6\{i:l\}(sth-es(sth)) authenticates 3 messages )
Date html generated:
2011_08_17-PM-07_52_10
Last ObjectModification:
2011_06_18-PM-01_46_32
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