Nuprl Lemma : st-lookup-distinct
∀[T:Id ─→ Type]. ∀[tab:secret-table(T)].
∀[x:Atom1]. ∀[n:ℕ||tab|| ].
((↑isl(st-lookup(tab;x)))
c∧ (outl(st-lookup(tab;x)) = <key(tab;n), data(tab;n)> ∈ (ℕ + Atom1 × data(T)))) supposing
((st-atom(tab;n) = x ∈ Atom1) 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,
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],
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 ∈ T
Lemmas :
assert_witness,
isl_wf,
nat_wf,
data_wf,
unit_wf2,
st-lookup_wf,
equal-wf-T-base,
st-atom_wf,
atom1_subtype_base,
le_wf,
st-ptr_wf,
int_seg_wf,
st-length_wf,
st-atoms-distinct_wf,
secret-table_wf,
Id_wf,
st-lookup-property,
st-lookup-outl,
subtype_base_sq,
int_subtype_base
\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:
2015_07_17-AM-08_57_09
Last ObjectModification:
2015_01_27-PM-01_03_18
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