{ 
[ses:SES]
[bss:Basic1 List]
[A:Id]
([es:EO+(Info)]. [thr:Thread].
([i:
||thr||]. [j:i].
(
(signature(thr[j]) released before thr[i])) supposing
((k:{j + 1..i
}. (
thr[k] 
Send)) and
(thr[j] Sign))) supposing
(loc(thr)= A and
(thr is one of bss at A))) supposing
((Protocol1(bss) A) and
Honest(A))
supposing Legal(bss) 
UniqueSignatures(bss)
supposing SecurityAxioms }
{ Proof }
Definitions occuring in Statement :
unique-sig-protocol: UniqueSignatures(bss),
ses-protocol1-legal: Legal(bss),
ses-protocol1: Protocol1(bss),
ses-protocol1-thread: (thr is one of bss at A),
ses-basic-sequence1: Basic1,
ses-thread-loc: loc(thr)= A,
ses-thread: Thread,
ses-axioms: SecurityAxioms,
release-before: (a released before e),
ses-honest: Honest(A),
ses-sig: signature(e),
ses-sign: Sign,
ses-send: Send,
ses-info: Info,
security-event-structure: SES,
in-eclass: e X,
event-ordering+: EO+(Info),
Id: Id,
select: l[i],
length: ||as||,
assert: b,
int_seg: {i..j},
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
not: A,
and: P Q,
apply: f a,
list: type List,
add: n + m,
natural_number: $n
Definitions :
es-interface-at: X@i,
intensional-universe: IType,
event-has*: e has* a,
isl: isl(x),
can-apply: can-apply(f;x),
ses-sig: signature(e),
cand: A c B,
release-before: (a released before e),
rec: rec(x.A[x]),
tree: Tree(E),
ses-send: Send,
minus: -n,
nil: [],
ses-action: Action(e),
Knd: Knd,
so_lambda: 
x.t[x],
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
tag-by: z
T,
or: P 
Q,
ldag: LabeledDAG(T),
labeled-graph: LabeledGraph(T),
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 
T2,
b-union: A 
B,
union: left + right,
bag: bag(T),
true: True,
filter: filter(P;l),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
lambda: x.A[x],
lelt: i 
j < k,
so_lambda: x y.t[x; y],
sdata: SecurityData,
ses-sign: Sign,
in-eclass: e X,
rationals: 
,
record-select: r.x,
infix_ap: x f y,
es-causl: (e < e'),
add: n + m,
select: l[i],
es-locl: (e <loc e'),
subtract: n - m,
event_ordering: EO,
fpf-cap: f(x)?z,
map: map(f;as),
es-E-interface: E(X),
ses-act: Act,
encryption-key: Key,
es-E: E,
l_exists: (
xL. P[x]),
pair: <a, b>,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
noncelike-signatures: noncelike-signatures(s;es;thr),
l_member: (x l),
l_all: (xL.P[x]),
l_contains: A B,
ses-legal-thread: Legal(thr)@A,
rev_implies: P 
Q,
iff: P 
Q,
pi1: fst(t),
ses-key-rel: MatchingKeys(k1;k2),
ycomb: Y,
ses-flow: ses-flow(s;es;a;e1;e2),
void: Void,
false: False,
exists: x:A. B[x],
dep-isect: Error :dep-isect,
record+: record+,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: b,
atom: Atom$n,
implies: P Q,
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,
le: A B,
ge: i 
j ,
not: A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A r B,
top: Top,
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
subtype: S T,
int: 
,
nat: ,
length: ||as||,
natural_number: $n,
int_seg: {i..j},
ses-thread-loc: loc(thr)= A,
ses-protocol1-thread: (thr is one of bss at A),
ses-thread: Thread,
ses-info: Info,
event-ordering+: EO+(Info),
ses-protocol1: Protocol1(bss),
apply: f a,
ses-honest: Honest(A),
Id: Id,
ses-protocol1-legal: Legal(bss),
unique-sig-protocol: UniqueSignatures(bss),
product: x:A B[x],
and: P Q,
universe: Type,
uimplies: b supposing a,
all: x:A. B[x],
function: x:A 
B[x],
isect: x:A. B[x],
uall: [x:A]. B[x],
ses-axioms: SecurityAxioms,
security-event-structure: SES,
equal: s = t,
prop: 
,
list: type List,
member: t T,
ses-basic-sequence1: Basic1,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
CollapseTHENA: Error :CollapseTHENA,
THENM: Error :THENM,
Auto: Error :Auto,
tactic: Error :tactic,
ses-nonce: PropertyN,
ses-ordering': ses-ordering'(s),
ses-ordering: PropertyO,
ses-thread-member: e thr,
es-loc: loc(e),
RepeatFor: Error :RepeatFor,
limited-type: LimitedType,
ses-private-key: PrivateKey(A),
ses-public-key: PublicKey(A),
es-le: e loc e' ,
es-causle: e c e',
bool: 
,
it: 
,
ses-info-flow: ->>,
rel_star: R^*,
event-has: (e has a),
guard: {T},
null: null(as),
squash: 
T,
strongwellfounded: SWellFounded(R[x; y]),
ses-new: New,
ses-crypt: cipherText(e),
ses-encrypt: Encrypt,
eclass-val: X(e),
fpf-dom: x dom(f),
pi2: snd(t),
ses-verify: Verify,
ses-decrypt: Decrypt,
ses-rcv: Rcv,
btrue: tt,
es-p-le: e p e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
sqequal: s ~ t,
sq_type: SQType(T),
so_apply: x[s],
iseg: l1 l2,
runEvents: runEvents(r),
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
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-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
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),
unit: Unit,
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-legal-sequence: Legal(pas) given prvt,
decidable: Dec(P),
IdLnk: IdLnk,
MaName: MaName,
consensus-state3: consensus-state3(T),
consensus-rcv: consensus-rcv(V;A),
append: as @ bs,
es-before: before(e),
es-le-before: loc(e),
cons: [car / cdr],
hd: hd(l),
last: last(L),
remove-repeats: remove-repeats(eq;L),
label: ...$L... t,
proper-iseg: L1 < L2,
gt: i > j
Lemmas :
bool_subtype_base,
es-causle_wf,
es-causle_transitivity,
add_wf,
decidable__lt,
ses-thread-weak-order,
list_subtype_base,
set_subtype_base,
squash_wf,
es-locl_irreflexivity,
ses-thread-order,
iseg_select2,
decidable__le,
es-le_wf,
iseg_member,
l_member_wf,
l_member_subtype,
iseg_wf,
es-le_weakening,
es-locl_transitivity2,
es-causl_irreflexivity,
es-causle_weakening,
es-causl_transitivity2,
decidable__equal_Id,
ses-R_wf,
ses-D_wf,
ses-S_wf,
ses-K_wf,
ses-nonce-disjoint_wf,
ses-flow-axiom_wf,
ses-V_wf,
ses-disjoint_wf,
ses-legal-thread-has*-signature,
noncelike-signatures_wf,
decidable_wf,
decidable__ex_int_seg,
decidable__es-E-equal,
event_ordering_wf,
record+_wf,
ses-legal-thread_wf,
l_contains_wf,
uiff_inversion,
subtype_base_sq,
atom2_subtype_base,
es-le-not-locl,
es-causle_weakening_locl,
es-causl_weakening,
es-causl_transitivity1,
bool_wf,
assert_elim,
true_wf,
ifthenelse_wf,
ses-rcv_wf,
ses-encrypt_wf,
encryption-key_wf,
ses-decrypt_wf,
ses-verify_wf,
ses-new_wf,
es-le-loc,
pi2_wf,
ses-action_wf,
es-causl_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
es-loc_wf,
guard_wf,
nat_ind_tp,
non_neg_length,
event-has_wf,
ses-info-flow_wf,
rel_star_wf,
ses-thread-member_wf,
le_wf,
ses-flow-axiom-ordering,
ses-ordering-ordering',
ses-nonce-from-ordering,
ses-thread_wf,
top_wf,
subtype_rel_wf,
member_wf,
ses-act_wf,
nat_wf,
length_wf_nat,
int_seg_wf,
ses-thread-loc_wf,
ses-protocol1-thread_wf,
ses-info_wf,
event-ordering+_wf,
ses-protocol1_wf,
ses-honest_wf,
Id_wf,
unique-sig-protocol_wf,
ses-protocol1-legal_wf,
ses-basic-sequence1_wf,
ses-axioms_wf,
security-event-structure_wf,
subtype_rel_list,
assert_wf,
ses-sign_wf,
in-eclass_wf,
eclass_wf,
es-E_wf,
select_wf,
event-ordering+_inc,
sdata_wf,
es-interface-top,
es-interface-subtype_rel2,
es-base-E_wf,
subtype_rel_self,
es-locl_wf,
subtype_rel_set,
length_wf1,
int_seg_properties,
not_wf,
ses-send_wf,
release-before_wf,
false_wf,
ses-sig_wf,
es-E-interface_wf,
event-has*_wf,
intensional-universe_wf
\mforall{}[ses:SES]
\mforall{}[bss:Basic1 List]
\mforall{}[A:Id]
(\mforall{}[es:EO+(Info)]. \mforall{}[thr:Thread].
(\mforall{}[i:\mBbbN{}||thr||]. \mforall{}[j:\mBbbN{}i].
(\mneg{}(signature(thr[j]) released before thr[i])) supposing
((\mforall{}k:\{j + 1..i\msupminus{}\}. (\mneg{}\muparrow{}thr[k] \mmember{}\msubb{} Send)) and
(\muparrow{}thr[j] \mmember{}\msubb{} Sign))) supposing
(loc(thr)= A and
(thr is one of bss at A))) supposing
((Protocol1(bss) A) and
Honest(A))
supposing Legal(bss) \mwedge{} UniqueSignatures(bss)
supposing SecurityAxioms
Date html generated:
2011_08_17-PM-07_46_03
Last ObjectModification:
2011_06_18-PM-01_41_10
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