Nuprl Lemma : ses-legal-thread-decrypt
∀s:SES
(ActionsDisjoint
⇒ PropertyD
⇒ (∀es:EO+(Info). ∀A:Id. ∀thr:Thread. ∀e:E.
(Legal(thr)@A
⇒ e ∈ thr ⇒ (∃a:Act. ((a <loc e) ∧ a ∈ thr ∧ (a has cipherText(e)))) supposing ↑e ∈b Decrypt))
supposing NoncesCiphersAndKeysDisjoint)
Proof
Definitions occuring in Statement :
ses-legal-thread: Legal(thr)@A,
ses-thread-member: e ∈ thr,
ses-thread: Thread,
ses-nonce-disjoint: NoncesCiphersAndKeysDisjoint,
ses-disjoint: ActionsDisjoint,
ses-D: PropertyD,
event-has: (e has a),
ses-act: Act,
ses-cipher: cipherText(e),
ses-decrypt: Decrypt,
ses-info: Info,
security-event-structure: SES,
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Lemmas :
eclass-val_wf,
ses-info_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
ses-new_wf,
assert_elim,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
subtype_base_sq,
bool_wf,
bool_subtype_base,
ses-sig_wf,
es-E-interface_wf,
ses-sign_wf,
sdata_wf,
Id_wf,
ses-crypt_wf,
ses-encrypt_wf,
encryption-key_wf,
ses-private_wf,
assert_witness,
ses-decrypt_wf,
exists_wf,
int_seg_wf,
length_wf,
ses-act_wf,
equal_wf,
select_wf,
sq_stable__le,
assert_wf,
all_wf,
l_contains_wf,
ses-used-atoms_wf,
cons_wf,
concat_wf,
map_wf,
le_wf,
less_than_wf,
list_wf,
ses-useable-atoms_wf,
less_than_transitivity2,
le_weakening2,
from-upto_wf,
set_wf,
subtract_wf,
es-locl_wf,
decidable__lt,
false_wf,
less-iff-le,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
decidable__le,
not-le-2,
zero-add,
add-zero,
le-add-cancel,
ses-D_wf,
ses-nonce-disjoint_wf,
ses-disjoint_wf,
security-event-structure_wf,
l_all_iff,
l_member_wf,
ses-cipher_wf,
member-used-atoms,
encryption-key-atoms_wf,
ses-decryption-key_wf,
or_wf,
ses-verify_wf,
ses-verify-sig_wf,
sdata-atoms_wf,
ses-verify-signed_wf,
ses-signed_wf,
ses-encrypted_wf,
ses-encryption-key_wf,
ses-send_wf,
cons_member,
member-concat,
member_map,
event-has_wf,
ses-thread-order,
lelt_wf,
squash_wf,
true_wf,
event_ordering_wf,
iff_weakening_equal,
ses-act-has-atom
Latex:
\mforall{}s:SES
(ActionsDisjoint
{}\mRightarrow{} PropertyD
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}A:Id. \mforall{}thr:Thread. \mforall{}e:E.
(Legal(thr)@A
{}\mRightarrow{} e \mmember{} thr {}\mRightarrow{} (\mexists{}a:Act. ((a <loc e) \mwedge{} a \mmember{} thr \mwedge{} (a has cipherText(e))))
supposing \muparrow{}e \mmember{}\msubb{} Decrypt))
supposing NoncesCiphersAndKeysDisjoint)
Date html generated:
2015_07_23-PM-00_11_22
Last ObjectModification:
2015_02_04-PM-03_36_37
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