Nuprl Lemma : st-length-encrypt
∀[T:Id ⟶ Type]. ∀[tab:secret-table(T)]. ∀[keyv:ℕ + Atom1 × data(T)]. (||encrypt(tab;keyv)|| = ||tab|| ∈ ℤ)
Proof
Definitions occuring in Statement :
st-encrypt: encrypt(tab;keyv),
st-length: ||tab|| ,
secret-table: secret-table(T),
data: data(T),
Id: Id,
nat: ℕ,
atom: Atom$n,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
secret-table: secret-table(T),
st-encrypt: encrypt(tab;keyv),
spreadn: spread3,
nat: ℕ,
st-length: ||tab|| ,
pi1: fst(t),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T}
Latex:
\mforall{}[T:Id {}\mrightarrow{} Type]. \mforall{}[tab:secret-table(T)]. \mforall{}[keyv:\mBbbN{} + Atom1 \mtimes{} data(T)].
(||encrypt(tab;keyv)|| = ||tab|| )
Date html generated:
2016_05_16-AM-10_03_57
Last ObjectModification:
2015_12_28-PM-09_30_10
Theory : new!event-ordering
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