{ 
[T:Id 
Type]. [tab:secret-table(T)].
[x:Atom1]. [n:
||tab|| ].
((
isl(st-lookup(tab;x)))
c
(outl(st-lookup(tab;x)) = <key(tab;n), data(tab;n)>)) supposing
((st-atom(tab;n) = x) and
(n 
ptr(tab)))
supposing atoms-distinct(tab) }
{ Proof }
Definitions occuring in Statement :
st-atoms-distinct: atoms-distinct(tab),
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],
cand: A c B,
le: A B,
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 :
pi1: fst(t),
bool: 
,
fpf: a:A fp-> B[a],
unit: Unit,
list: type List,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
uiff: uiff(P;Q),
less_than: a < b,
subtype_rel: A 
r B,
lambda: 
x.A[x],
st-data: data(tab;n),
st-key: key(tab;n),
outl: outl(x),
st-lookup: st-lookup(tab;x),
isl: isl(x),
union: left + right,
data: data(T),
so_lambda: 
x.t[x],
axiom: Ax,
void: Void,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
assert: b,
cand: A c B,
st-atom: st-atom(tab;n),
limited-type: LimitedType,
false: False,
not: 
A,
st-ptr: ptr(tab),
rationals: 
,
and: P Q,
lelt: i j < k,
le: A B,
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
subtype: S T,
nat: ,
st-length: ||tab|| ,
natural_number: $n,
int_seg: {i..j},
pair: <a, b>,
int: 
,
implies: P 
Q,
atom: Atom$n,
product: x:A B[x],
prop: 
,
st-atoms-distinct: atoms-distinct(tab),
uimplies: b supposing a,
isect: 
x:A. B[x],
all: x:A. B[x],
uall: [x:A]. B[x],
secret-table: secret-table(T),
Id: Id,
function: x:A B[x],
equal: s = t,
universe: Type,
member: t 
T,
tactic: Error :tactic,
iff: P 
Q,
rev_implies: P Q,
exists: 
x:A. B[x],
guard: {T},
sq_type: SQType(T)
Lemmas :
st-lookup-outl,
subtype_base_sq,
int_subtype_base,
st-lookup-property,
not_wf,
outl_wf,
nat_wf,
data_wf,
unit_wf,
st-lookup_wf,
st-data_wf,
st-key_wf,
st-length_wf,
st-ptr_wf,
true_wf,
isl_wf,
ifthenelse_wf,
false_wf,
assert_wf,
assert_witness,
pair_wf,
st-atom_wf,
int_seg_properties,
le_wf,
int_seg_wf,
st-atoms-distinct_wf,
secret-table_wf,
Id_wf
\mforall{}[T:Id {}\mrightarrow{} Type]. \mforall{}[tab:secret-table(T)].
\mforall{}[x:Atom1]. \mforall{}[n:\mBbbN{}||tab|| ].
((\muparrow{}isl(st-lookup(tab;x))) c\mwedge{} (outl(st-lookup(tab;x)) = <key(tab;n), data(tab;n)>)) supposing
((st-atom(tab;n) = x) and
(n \mleq{} ptr(tab)))
supposing atoms-distinct(tab)
Date html generated:
2011_08_16-AM-11_00_20
Last ObjectModification:
2011_06_18-AM-09_33_55
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