Nuprl Lemma : ses-legal-thread-has*-signature
∀s:SES
(SecurityAxioms
⇒ (∀es:EO+(Info). ∀A:Id. ∀thr:Thread.
((Legal(thr)@A ∧ noncelike-signatures(s;es;thr))
⇒ (∀sg:E(Sign). ∀e:Act.
(e ∈ thr
⇒ e has* signature(sg)
⇒ (∃e':E. ((e' <loc e) ∧ Action(e') ∧ e' has* signature(sg) ∧ e' ∈ thr)) ∨ (e = sg ∈ E)
supposing ∀e':E
((e' < e)
⇒ Action(e')
⇒ e' has* signature(sg)
⇒ ((loc(e') = A ∈ Id) ∧ (¬↑e' ∈b Send))))))))
Proof
Definitions occuring in Statement :
noncelike-signatures: noncelike-signatures(s;es;thr),
ses-legal-thread: Legal(thr)@A,
ses-thread-member: e ∈ thr,
ses-thread: Thread,
ses-axioms: SecurityAxioms,
event-has*: e has* a,
ses-act: Act,
ses-action: Action(e),
ses-sig: signature(e),
ses-sign: Sign,
ses-send: Send,
ses-info: Info,
security-event-structure: SES,
es-E-interface: E(X),
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
sq_stable_from_decidable,
ses-action_wf,
decidable__ses-action,
assert_wf,
in-eclass_wf,
ses-send_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
sdata_wf,
event-has*_wf,
ses-sig_wf,
es-causl_wf,
all_wf,
es-loc_wf,
not_wf,
ses-thread-member_wf,
ses-act_wf,
es-E-interface_wf,
ses-sign_wf,
ses-legal-thread_wf,
noncelike-signatures_wf,
ses-thread_wf,
Id_wf,
event-ordering+_wf,
ses-info_wf,
ses-axioms_wf,
security-event-structure_wf,
es-causl-swellfnd,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
event-has_wf,
infix_ap_wf,
rel_exp_wf,
ses-info-flow_wf,
le_weakening2,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
or_wf,
exists_wf,
es-locl_wf,
equal_wf,
set_wf,
less_than_wf,
primrec-wf2,
es-le_wf,
int_seg_subtype-nat,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
sq_stable__le,
add-mul-special,
zero-mul,
ses-legal-thread-has-atom,
event-has*-iff,
subtype_rel_dep_function,
member-useable-atoms,
ses-rcv_wf,
es-causl_transitivity2,
es-causle_weakening_locl,
ses-act-has-atom,
ses-encrypt_wf,
encryption-key_wf,
ses-decrypt_wf,
ses-verify_wf,
ses-new_wf,
bool_wf,
eqtt_to_assert,
l_member_wf,
squash_wf,
true_wf,
list_wf,
sdata-atoms_wf,
iff_weakening_equal,
ses-useable-atoms_wf,
eqff_to_assert,
assert_elim,
bfalse_wf,
and_wf,
bnot_wf,
btrue_neq_bfalse,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
ses-legal-thread-decrypt,
ses-used-atoms_wf,
decidable__or,
decidable__l_member,
decidable__atom_equal_1,
member-used-atoms,
encryption-key-atoms_wf,
ses-encryption-key_wf,
ses-signed_wf,
ses-verify-sig_wf,
ses-verify-signed_wf,
ses-cipher_wf,
ses-decryption-key_wf,
eclass-val_wf,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening,
sq_stable__l_member,
ses-crypt_wf,
ses-decrypted_wf,
rel_exp_iff,
rel_star_wf,
class-value-has_wf,
free-from-atom_wf,
event-has*-transitive-encrypt,
atom1_subtype_base,
ses-cipher-unique,
ses-flow-axiom-ordering,
int_subtype_base,
event-has_functionality,
member_wf,
ses-info-flow-exp_functionality,
le-add-cancel2,
decidable__es-E-equal,
es-le-self
Latex:
\mforall{}s:SES
(SecurityAxioms
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}A:Id. \mforall{}thr:Thread.
((Legal(thr)@A \mwedge{} noncelike-signatures(s;es;thr))
{}\mRightarrow{} (\mforall{}sg:E(Sign). \mforall{}e:Act.
(e \mmember{} thr
{}\mRightarrow{} e has* signature(sg)
{}\mRightarrow{} (\mexists{}e':E. ((e' <loc e) \mwedge{} Action(e') \mwedge{} e' has* signature(sg) \mwedge{} e' \mmember{} thr)) \mvee{} (e = sg)
supposing \mforall{}e':E
((e' < e)
{}\mRightarrow{} Action(e')
{}\mRightarrow{} e' has* signature(sg)
{}\mRightarrow{} ((loc(e') = A) \mwedge{} (\mneg{}\muparrow{}e' \mmember{}\msubb{} Send))))))))
Date html generated:
2015_07_23-PM-00_13_30
Last ObjectModification:
2015_02_04-PM-03_50_21
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