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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