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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cand: A c∧ B,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
st-atoms-distinct: atoms-distinct(tab)
Latex:
\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:
2016_05_16-AM-10_03_08
Last ObjectModification:
2015_12_28-PM-09_27_51
Theory : new!event-ordering
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