{ 
[s:SES]
[es:EO+(Info)]. [a,b:E(Encrypt)].
Encrypt(a) = Encrypt(b) supposing cipherText(a) = cipherText(b)
supposing PropertyO }
{ Proof }
Definitions occuring in Statement :
ses-ordering: PropertyO,
ses-crypt: cipherText(e),
ses-encrypt: Encrypt,
ses-info: Info,
security-event-structure: SES,
encryption-key: Key,
sdata: SecurityData,
es-E-interface: E(X),
eclass-val: X(e),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: [x:A]. B[x],
product: x:A 
B[x],
equal: s = t,
atom: Atom$n
Definitions :
tactic: Error :tactic,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
equal: s = t,
member: t 
T,
function: x:A 
B[x],
all: x:A. B[x],
ses-ordering: PropertyO,
security-event-structure: SES,
product: x:A B[x],
prop: 
,
uimplies: b supposing a,
event-ordering+: EO+(Info),
ses-info: Info,
and: P 
Q,
implies: P 
Q,
or: P 
Q,
union: left + right,
exists: 
x:A. B[x],
es-le: e 
loc e' ,
es-locl: (e <loc e'),
es-causl: (e < e'),
event-has*: e has* a,
infix_ap: x f y,
record-select: r.x,
es-E-interface: E(X),
ses-encrypt: Encrypt,
top: Top,
record+: record+,
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
dep-isect: Error :dep-isect,
eclass: EClass(A[eo; e]),
sdata: SecurityData,
encryption-key: Key,
atom: Atom$n,
so_lambda: 
x y.t[x; y],
subtype_rel: A 
r B,
es-E: E,
event_ordering: EO,
lambda: x.A[x],
ifthenelse: if b then t else f fi ,
token: "$token",
apply: f a,
atom: Atom,
universe: Type,
subtype: S T,
void: Void,
assert: 
b,
set: {x:A| B[x]} ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
limited-type: LimitedType,
ses-crypt: cipherText(e),
eclass-val: X(e),
axiom: Ax,
uiff: uiff(P;Q),
less_than: a < b,
not: 
A,
ge: i 
j ,
le: A B,
strong-subtype: strong-subtype(A;B),
fpf: a:A fp-> B[a],
pair: <a, b>,
bool: 
,
RepeatFor: Error :RepeatFor,
D: Error :D,
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
ExRepD: Error :ExRepD,
CollapseTHENA: Error :CollapseTHENA,
MaAuto: Error :MaAuto,
strongwellfounded: SWellFounded(R[x; y]),
guard: {T},
nat: 
,
add: n + m,
int: 
,
rationals: 
,
real: 
,
false: False,
natural_number: $n,
grp_car: |g|,
subtract: n - m,
minus: -n,
l_member: (x l),
list: type List,
Knd: Knd,
locl: locl(a),
append: as @ bs,
so_apply: x[s],
Id: Id,
IdLnk: IdLnk,
record: record(x.T[x]),
event-has: (e has a),
ses-send: Send,
ses-sign: Sign,
ses-sig: signature(e),
ses-new: New,
rel_star: R^*,
class-value-has: X(e) has a,
ses-rcv: Rcv,
ses-decrypt: Decrypt,
ses-verify: Verify,
RepUR: Error :RepUR,
free-from-atom: x:T||a,
in-eclass: e 
X,
true: True,
sq_type: SQType(T),
btrue: tt,
cand: A c B,
iff: P 
Q,
rev_implies: P Q,
tree: Tree(E),
rec: rec(x.A[x]),
Subst': Error :Subst',
sqequal: s ~ t,
ses-encrypted: plainText(e),
ses-encryption-key: key(e),
es-causle: e c e',
causal-predecessor: causal-predecessor(es;p),
es-p-locl: e p< e',
es-p-le: e p e',
so_lambda: x.t[x],
squash: 
T,
so_apply: x[s1;s2],
can-apply: can-apply(f;x),
isl: isl(x)
Lemmas :
atom1_subtype_base,
union_subtype_base,
atom2_subtype_base,
product_subtype_base,
sdata_subtype_base,
set_subtype_base,
squash_wf,
es-causle_weakening,
es-causl_transitivity2,
es-causl_weakening,
es-causle_wf,
es-causle_weakening_locl,
atom1_sq,
atom_sq,
ses-encryption-key_wf,
free-from-atom-pair-iff,
iff_weakening_uiff,
ses-encrypted_wf,
free-from-atom_wf1,
assert_wf,
ifthenelse_wf,
true_wf,
subtype_base_sq,
bool_subtype_base,
bool_wf,
assert_elim,
in-eclass_wf,
ses-new_wf,
ses-verify_wf,
Id_wf,
ses-sign_wf,
ses-decrypt_wf,
ses-rcv_wf,
class-value-has_wf,
ses-send_wf,
event-has_wf,
uiff_inversion,
es-causl_wf,
false_wf,
not_wf,
le_wf,
nat_ind_tp,
nat_wf,
guard_wf,
es-causl-swellfnd,
nat_properties,
ge_wf,
eclass-val_wf,
ses-crypt_wf,
security-event-structure_wf,
ses-ordering_wf,
es-E-interface_wf,
eclass_wf,
member_wf,
es-interface-top,
es-interface-subtype_rel2,
ses-encrypt_wf,
subtype_rel_self,
event-ordering+_inc,
event-ordering+_wf,
subtype_rel_wf,
sdata_wf,
encryption-key_wf,
top_wf,
es-E_wf,
ses-info_wf
\mforall{}[s:SES]
\mforall{}[es:EO+(Info)]. \mforall{}[a,b:E(Encrypt)].
Encrypt(a) = Encrypt(b) supposing cipherText(a) = cipherText(b)
supposing PropertyO
Date html generated:
2011_08_17-PM-07_24_03
Last ObjectModification:
2011_06_18-PM-01_17_32
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