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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
secret-table: secret-table(T),
st-atom: st-atom(tab;n),
st-ptr: ptr(tab),
st-length: ||tab|| ,
st-lookup: st-lookup(tab;x),
spreadn: spread3,
pi1: fst(t),
pi2: snd(t),
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
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,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
assert: ↑b,
rev_implies: P ⇐ Q,
or: P ∨ Q,
true: True,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
sq_type: SQType(T),
isl: isl(x),
let: let,
exposed-bfalse: exposed-bfalse,
squash: ↓T,
less_than': less_than'(a;b),
decidable: Dec(P),
cand: A c∧ B,
bnot: ¬bb
Latex:
\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:
2016_05_16-AM-10_02_37
Last ObjectModification:
2016_01_17-PM-01_24_01
Theory : new!event-ordering
Home
Index