Nuprl Lemma : st-lookup-property
∀[T:Id ─→ Type]
∀tab:secret-table(T). ∀x:Atom1.
(↑isl(st-lookup(tab;x)) ⇐⇒ ∃n:ℕ||tab|| . ((n ≤ ptr(tab)) ∧ (st-atom(tab;n) = x ∈ Atom1)))
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,
int_seg: {i..j-},
atom: Atom$n,
assert: ↑b,
isl: isl(x),
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 ∈ T
Lemmas :
nat_wf,
secret-table_wf,
Id_wf,
mu_wf,
le_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
le_wf,
eqtt_to_assert,
assert_of_le_int,
bor_wf,
lt_int_wf,
btrue_wf,
less_than_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
eq_atom_wf1,
lelt_wf,
data_wf,
iff_transitivity,
or_wf,
true_wf,
iff_weakening_uiff,
assert_of_bor,
less_than_irreflexivity,
mu-property,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
false_wf,
exists_wf,
int_seg_wf,
atom1_subtype_base,
bnot_thru_bor,
band_wf,
squash_wf,
bnot_of_lt_int,
assert_of_band,
int_seg_subtype-nat,
assert_of_eq_atom1,
less_than_transitivity1,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom1
\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:
2015_07_17-AM-08_56_53
Last ObjectModification:
2015_01_27-PM-01_05_07
Home
Index