Nuprl Lemma : st-lookup_wf
∀[T:Id ⟶ Type]. ∀[tab:secret-table(T)]. ∀[x:Atom1]. (st-lookup(tab;x) ∈ ℕ + Atom1 × data(T)?)
Proof
Definitions occuring in Statement :
st-lookup: st-lookup(tab;x)
,
secret-table: secret-table(T)
,
data: data(T)
,
Id: Id
,
nat: ℕ
,
atom: Atom$n
,
uall: ∀[x:A]. B[x]
,
unit: Unit
,
member: t ∈ T
,
function: x:A ⟶ B[x]
,
product: x:A × B[x]
,
union: left + right
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
secret-table: secret-table(T)
,
st-lookup: st-lookup(tab;x)
,
spreadn: spread3,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
so_lambda: λ2x.t[x]
,
nat: ℕ
,
exposed-bfalse: exposed-bfalse
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
iff: P
⇐⇒ Q
,
prop: ℙ
,
rev_implies: P
⇐ Q
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bor: p ∨bq
,
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
,
so_apply: x[s]
,
subtype_rel: A ⊆r B
,
true: True
Latex:
\mforall{}[T:Id {}\mrightarrow{} Type]. \mforall{}[tab:secret-table(T)]. \mforall{}[x:Atom1]. (st-lookup(tab;x) \mmember{} \mBbbN{} + Atom1 \mtimes{} data(T)?)
Date html generated:
2016_05_16-AM-10_01_57
Last ObjectModification:
2016_01_17-PM-01_22_18
Theory : new!event-ordering
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