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
Lemmas :
nat_wf,
data_wf,
lt_int_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
less_than_wf,
le_int_wf,
le_wf,
bnot_wf,
lelt_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
eq_int_wf,
equal_wf,
sq_stable__le,
less_than_transitivity2,
le_weakening,
and_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
subtype_top,
not_wf,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
\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:
2015_07_17-AM-08_57_24
Last ObjectModification:
2015_01_27-PM-01_03_27
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