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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
secret-table: secret-table(T),
st-lookup: st-lookup(tab;x),
st-atom: st-atom(tab;n),
st-ptr: ptr(tab),
st-length: ||tab|| ,
spreadn: spread3,
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
nat: ℕ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
le: A ≤ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
isl: isl(x),
outl: outl(x),
st-data: data(tab;n),
st-key: key(tab;n),
let: let,
exposed-bfalse: exposed-bfalse,
squash: ↓T,
cand: A c∧ B
Latex:
\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:
2016_05_16-AM-10_02_53
Last ObjectModification:
2016_01_17-PM-01_23_43
Theory : new!event-ordering
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