Nuprl Lemma : st-atom-encrypt
∀[T:Id ⟶ Type]. ∀[tab:secret-table(T)]. ∀[keyv:ℕ + Atom1 × data(T)]. ∀[n:ℕ||tab|| ].
(st-atom(encrypt(tab;keyv);n) = st-atom(tab;n) ∈ Atom1)
Proof
Definitions occuring in Statement :
st-encrypt: encrypt(tab;keyv),
st-atom: st-atom(tab;n),
st-length: ||tab|| ,
secret-table: secret-table(T),
data: data(T),
Id: Id,
int_seg: {i..j-},
nat: ℕ,
atom: Atom$n,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
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,
secret-table: secret-table(T),
st-atom: st-atom(tab;n),
st-encrypt: encrypt(tab;keyv),
spreadn: spread3,
pi2: snd(t),
update: f[x:=v],
nat: ℕ,
st-length: ||tab|| ,
pi1: fst(t),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[T:Id {}\mrightarrow{} Type]. \mforall{}[tab:secret-table(T)]. \mforall{}[keyv:\mBbbN{} + Atom1 \mtimes{} data(T)]. \mforall{}[n:\mBbbN{}||tab|| ].
(st-atom(encrypt(tab;keyv);n) = st-atom(tab;n))
Date html generated:
2016_05_16-AM-10_04_07
Last ObjectModification:
2016_01_17-PM-01_21_16
Theory : new!event-ordering
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