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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
ses-thread: Thread,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
ses-act: Act,
so_lambda: λ2x.t[x],
so_apply: x[s],
security-theory: SecurityTheory,
sth-es: sth-es(s),
pi1: fst(t)
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:
2016_05_17-PM-00_46_39
Last ObjectModification:
2016_01_18-AM-07_41_04
Theory : event-logic-applications
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