{ 
[T:Id 
Type]
tab:secret-table(T). x:Atom1.
(
isl(st-lookup(tab;x))
n:
||tab|| . ((n 
ptr(tab)) 
(st-atom(tab;n) = x))) }
{ Proof }
Definitions occuring in Statement :
st-lookup: st-lookup(tab;x),
st-atom: st-atom(tab;n),
st-ptr: ptr(tab),
st-length: ||tab|| ,
secret-table: secret-table(T),
Id: Id,
isl: isl(x),
assert: b,
int_seg: {i..j
},
uall: [x:A]. B[x],
le: A B,
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
and: P Q,
function: x:A B[x],
natural_number: $n,
universe: Type,
equal: s = t,
atom: Atom$n
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
st-lookup: st-lookup(tab;x),
st-length: ||tab|| ,
st-ptr: ptr(tab),
st-atom: st-atom(tab;n),
spreadn: spread3,
pi1: fst(t),
pi2: snd(t),
member: t 
T,
implies: P Q,
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,
iff: P Q,
isl: isl(x),
false: False,
rev_implies: P Q,
let: let,
squash: 
T,
not: 
A,
le: A B,
secret-table: secret-table(T),
uimplies: b supposing a,
bool: 
,
unit: Unit,
guard: {T},
sq_type: SQType(T),
so_apply: x[s],
it: 
Lemmas :
nat_wf,
secret-table_wf,
Id_wf,
mu_wf,
le_int_wf,
bool_wf,
iff_weakening_uiff,
le_wf,
uiff_transitivity,
assert_wf,
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,
data_wf,
bnot_of_lt_int,
mu-property,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__assert,
decidable_wf,
false_wf,
int_seg_wf,
band_wf,
true_wf,
assert_of_bor,
or_functionality_wrt_uiff,
bnot_thru_bor,
squash_wf,
assert_of_band,
and_functionality_wrt_uiff,
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.
(\muparrow{}isl(st-lookup(tab;x)) \mLeftarrow{}{}\mRightarrow{} \mexists{}n:\mBbbN{}||tab|| . ((n \mleq{} ptr(tab)) \mwedge{} (st-atom(tab;n) = x)))
Date html generated:
2011_08_16-AM-10_59_51
Last ObjectModification:
2011_06_18-AM-09_33_37
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