{ 
[T:Id 
Type]. [tab:secret-table(T)]. [keyv:
+ Atom1 
data(T)].
[n:||tab|| ].
(st-atom(encrypt(tab;keyv);n) = st-atom(tab;n)) }
{ Proof }
Definitions occuring in Statement :
st-encrypt: encrypt(tab;keyv),
st-atom: st-atom(tab;n),
st-length: ||tab|| ,
secret-table: secret-table(T),
data: data(T),
Id: Id,
int_seg: {i..j
},
nat: ,
uall: [x:A]. B[x],
function: x:A B[x],
product: x:A B[x],
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t,
atom: Atom$n
Definitions :
uall: [x:A]. B[x],
int_seg: {i..j},
st-atom: st-atom(tab;n),
st-encrypt: encrypt(tab;keyv),
member: t 
T,
pi2: snd(t),
spreadn: spread3,
update: f[x:=v],
le: A 
B,
prop: 
,
top: Top,
lelt: i j < k,
and: P 
Q,
not: 
A,
implies: P 
Q,
false: False,
all: x:A. B[x],
subtype: S 
T,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
pi1: fst(t),
squash: 
T,
true: True,
secret-table: secret-table(T),
nat: ,
st-length: ||tab|| ,
bool: 
,
unit: Unit,
iff: P 
Q,
uimplies: b supposing a,
it: 
Lemmas :
int_seg_wf,
st-length_wf,
nat_wf,
data_wf,
secret-table_wf,
Id_wf,
lt_int_wf,
bool_wf,
assert_wf,
le_wf,
le_int_wf,
bnot_wf,
pi1_wf_top,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
eq_int_wf,
not_wf,
assert_of_eq_int,
assert_of_bnot,
not_functionality_wrt_uiff
\mforall{}[T:Id {}\mrightarrow{} Type]. \mforall{}[tab:secret-table(T)]. \mforall{}[keyv:\mBbbN{} + Atom1 \mtimes{} data(T)]. \mforall{}[n:\mBbbN{}||tab|| ].
(st-atom(encrypt(tab;keyv);n) = st-atom(tab;n))
Date html generated:
2011_08_16-AM-11_00_57
Last ObjectModification:
2011_06_18-AM-09_34_25
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