Nuprl Lemma : signature-release-lemma
∀[ses:SES]
∀[bss:Basic1 List]
∀[A:Id]
(∀[es:EO+(Info)]. ∀[thr:Thread].
(∀[i:ℕ||thr||]. ∀[j:ℕi].
(¬(signature(thr[j]) released before thr[i])) supposing
((∀k:{j + 1..i-}. (¬↑thr[k] ∈b Send)) and
(↑thr[j] ∈b Sign))) supposing
(loc(thr)= A and
(thr is one of bss at A))) supposing
((Protocol1(bss) A) and
Honest(A))
supposing Legal(bss) ∧ UniqueSignatures(bss)
supposing SecurityAxioms
Proof
Definitions occuring in Statement :
unique-sig-protocol: UniqueSignatures(bss),
ses-protocol1-legal: Legal(bss),
ses-protocol1: Protocol1(bss),
ses-protocol1-thread: (thr is one of bss at A),
ses-basic-sequence1: Basic1,
ses-thread-loc: loc(thr)= A,
ses-thread: Thread,
ses-axioms: SecurityAxioms,
release-before: (a released before e),
ses-honest: Honest(A),
ses-sig: signature(e),
ses-sign: Sign,
ses-send: Send,
ses-info: Info,
security-event-structure: SES,
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
Id: Id,
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q,
apply: f a,
add: n + m,
natural_number: $n
Lemmas :
release-before_wf,
ses-sig_wf,
select_wf,
ses-act_wf,
sq_stable__le,
less_than_transitivity2,
length_wf,
le_weakening2,
assert_wf,
in-eclass_wf,
ses-sign_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
sdata_wf,
all_wf,
int_seg_wf,
not_wf,
ses-send_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
zero-add,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
ses-thread-loc_wf,
ses-protocol1-thread_wf,
ses-thread_wf,
event-ordering+_wf,
ses-info_wf,
ses-protocol1_wf,
ses-honest_wf,
Id_wf,
ses-protocol1-legal_wf,
unique-sig-protocol_wf,
list_wf,
ses-basic-sequence1_wf,
ses-axioms_wf,
security-event-structure_wf,
ses-flow-axiom-ordering,
ses-ordering-ordering',
ses-nonce-from-ordering,
lelt_wf,
equal_wf,
es-causl-swellfnd,
less_than_transitivity1,
less_than_irreflexivity,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
es-causl_wf,
event-has*_wf,
ses-action_wf,
int_seg_subtype-nat,
es-loc_wf,
es-locl_wf,
ses-thread-member_wf,
decidable__lt,
not-equal-2,
minus-minus,
le-add-cancel-alt,
less-iff-le,
set_wf,
less_than_wf,
primrec-wf2,
add-mul-special,
zero-mul,
iff_weakening_equal,
true_wf,
squash_wf,
pi2_wf,
and_wf,
es-le-loc,
ses-new_wf,
ses-verify_wf,
ses-decrypt_wf,
encryption-key_wf,
ses-encrypt_wf,
ses-rcv_wf,
or_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
assert_elim,
es-le-not-locl,
btrue_neq_bfalse,
not_assert_elim,
es-causle_weakening_locl,
es-causl_transitivity1,
decidable__exists_int_seg,
decidable__es-E-equal,
ses-legal-thread-has*-signature,
decidable__equal_Id,
es-le_weakening,
es-causl_transitivity2,
es-causl_irreflexivity,
es-causle_weakening,
es-causl_weakening,
es-locl_transitivity2,
iseg_member,
equal_functionality_wrt_subtype_rel2,
iseg_select2,
le-add-cancel2,
ses-thread-order,
es-locl_irreflexivity,
es-locl_transitivity1,
es-le_weakening_eq,
es-le_transitivity,
ses-thread-weak-order,
es-causle_wf,
es-causle_weakening_eq,
equal-wf-base,
es-le_wf
Latex:
\mforall{}[ses:SES]
\mforall{}[bss:Basic1 List]
\mforall{}[A:Id]
(\mforall{}[es:EO+(Info)]. \mforall{}[thr:Thread].
(\mforall{}[i:\mBbbN{}||thr||]. \mforall{}[j:\mBbbN{}i].
(\mneg{}(signature(thr[j]) released before thr[i])) supposing
((\mforall{}k:\{j + 1..i\msupminus{}\}. (\mneg{}\muparrow{}thr[k] \mmember{}\msubb{} Send)) and
(\muparrow{}thr[j] \mmember{}\msubb{} Sign))) supposing
(loc(thr)= A and
(thr is one of bss at A))) supposing
((Protocol1(bss) A) and
Honest(A))
supposing Legal(bss) \mwedge{} UniqueSignatures(bss)
supposing SecurityAxioms
Date html generated:
2015_07_23-PM-00_19_31
Last ObjectModification:
2015_07_16-AM-09_36_58
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