Nuprl Lemma : st-lookup-outl
∀[T:Id ─→ Type]
∀tab:secret-table(T). ∀x:Atom1.
∃n:ℕ||tab||
((n ≤ ptr(tab))
∧ (st-atom(tab;n) = x ∈ Atom1)
∧ (outl(st-lookup(tab;x)) = <key(tab;n), data(tab;n)> ∈ (ℕ + Atom1 × data(T))))
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,
int_seg: {i..j-},
nat: ℕ,
atom: Atom$n,
outl: outl(x),
assert: ↑b,
isl: isl(x),
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 ∈ T
Lemmas :
mu_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
bor_wf,
lt_int_wf,
btrue_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
eq_atom_wf1,
decidable__lt,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
lelt_wf,
data_wf,
nat_wf,
iff_transitivity,
assert_wf,
or_wf,
less_than_wf,
true_wf,
iff_weakening_uiff,
assert_of_bor,
assert_of_lt_int,
add-mul-special,
zero-mul,
add-zero,
add-associates,
mu-property,
set_subtype_base,
int_subtype_base,
equal-wf-T-base,
bnot_wf,
uiff_transitivity,
assert_functionality_wrt_uiff,
bnot_thru_bor,
band_wf,
squash_wf,
bnot_of_lt_int,
bnot_of_le_int,
assert_of_band,
pair_eta_rw,
iff_weakening_equal,
atom1_subtype_base,
less_than_transitivity1,
less_than_irreflexivity,
uall_wf,
isect_wf,
not_wf,
assert_of_eq_atom1
\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:
2015_07_17-AM-08_57_02
Last ObjectModification:
2015_02_04-PM-06_28_19
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