{ 
[T:Id 
Type]
tab:secret-table(T). x:Atom1.
n:
||tab||
((n 
ptr(tab))
(st-atom(tab;n) = x)
(outl(st-lookup(tab;x)) = <key(tab;n), data(tab;n)>))
supposing 
isl(st-lookup(tab;x)) }
{ Proof }
Definitions occuring in Statement :
st-lookup: st-lookup(tab;x),
st-data: data(tab;n),
st-key: key(tab;n),
st-atom: st-atom(tab;n),
st-ptr: ptr(tab),
st-length: ||tab|| ,
secret-table: secret-table(T),
data: data(T),
Id: Id,
outl: outl(x),
isl: isl(x),
assert: b,
int_seg: {i..j
},
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
and: P Q,
function: x:A B[x],
pair: <a, b>,
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],
all: x:A. B[x],
uimplies: b supposing a,
st-lookup: st-lookup(tab;x),
st-length: ||tab|| ,
st-ptr: ptr(tab),
st-atom: st-atom(tab;n),
member: t 
T,
implies: P 
Q,
spreadn: spread3,
pi1: fst(t),
pi2: snd(t),
int_seg: {i..j},
bor: p 
q,
btrue: tt,
prop: 
,
and: P Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
top: Top,
lelt: i j < k,
subtype: S 
T,
exists: x:A. B[x],
assert: b,
true: True,
nat: ,
so_lambda: 
x.t[x],
or: P Q,
isl: isl(x),
outl: outl(x),
false: False,
let: let,
st-key: key(tab;n),
st-data: data(tab;n),
squash: 
T,
not: 
A,
le: A B,
secret-table: secret-table(T),
bool: 
,
unit: Unit,
iff: P 
Q,
guard: {T},
sq_type: SQType(T),
so_apply: x[s],
it: 
Lemmas :
assert_witness,
isl_wf,
nat_wf,
data_wf,
unit_wf,
st-lookup_wf,
assert_wf,
secret-table_wf,
Id_wf,
mu_wf,
le_int_wf,
bool_wf,
iff_weakening_uiff,
le_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
bor_wf,
lt_int_wf,
btrue_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
eq_atom_wf1,
pi1_wf_top,
bnot_of_lt_int,
mu-property,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__assert,
decidable_wf,
false_wf,
band_wf,
true_wf,
assert_of_bor,
or_functionality_wrt_uiff,
bnot_thru_bor,
squash_wf,
assert_of_band,
and_functionality_wrt_uiff,
pi2_wf,
assert_of_eq_atom1,
not_wf,
assert_of_bnot,
not_functionality_wrt_uiff
\mforall{}[T:Id {}\mrightarrow{} Type]
\mforall{}tab:secret-table(T). \mforall{}x:Atom1.
\mexists{}n:\mBbbN{}||tab||
((n \mleq{} ptr(tab)) \mwedge{} (st-atom(tab;n) = x) \mwedge{} (outl(st-lookup(tab;x)) = <key(tab;n), data(tab;n)>))
supposing \muparrow{}isl(st-lookup(tab;x))
Date html generated:
2011_08_16-AM-11_00_02
Last ObjectModification:
2011_06_18-AM-09_33_43
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