Nuprl Lemma : nonce-release-lemma2
∀[s:SecurityTheory]. ∀[bss:Basic1 List].
∀[A:Id]
(∀[es:EO+(Info)]. ∀[thr:Thread].
(∀[i:ℕ||thr||]. ∀[j:ℕi].
(¬(New(thr[j]) released before thr[i])) supposing
((∀k:{j + 1..i-}. (¬↑thr[k] ∈b Send)) and
(↑thr[j] ∈b New))) supposing
(loc(thr)= A and
(thr is one of bss at A))) supposing
((Protocol1(bss) A) and
Honest(A))
supposing Legal(bss)
Proof
Definitions occuring in Statement :
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,
sth-es: sth-es(s),
security-theory: SecurityTheory,
release-before: (a released before e),
ses-honest: Honest(A),
ses-send: Send,
ses-new: New,
ses-info: Info,
eclass-val: X(e),
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,
apply: f a,
add: n + m,
natural_number: $n
Lemmas :
release-before_wf,
sth-es_wf,
eclass-val_wf,
ses-info_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
ses-new_wf,
select_wf,
ses-act_wf,
sq_stable__le,
less_than_transitivity2,
length_wf,
le_weakening2,
all_wf,
int_seg_wf,
not_wf,
assert_wf,
in-eclass_wf,
ses-send_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
sdata_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,
ses-protocol1_wf,
ses-honest_wf,
Id_wf,
ses-protocol1-legal_wf,
list_wf,
ses-basic-sequence1_wf,
security-theory_wf,
nonce-release-lemma
Latex:
\mforall{}[s:SecurityTheory]. \mforall{}[bss:Basic1 List].
\mforall{}[A:Id]
(\mforall{}[es:EO+(Info)]. \mforall{}[thr:Thread].
(\mforall{}[i:\mBbbN{}||thr||]. \mforall{}[j:\mBbbN{}i].
(\mneg{}(New(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{} New))) supposing
(loc(thr)= A and
(thr is one of bss at A))) supposing
((Protocol1(bss) A) and
Honest(A))
supposing Legal(bss)
Date html generated:
2015_07_23-PM-00_19_35
Last ObjectModification:
2015_01_29-AM-01_31_28
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