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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
ses-act: Act,
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
squash: ↓T,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
less_than: a < b,
es-E-interface: E(X),
infix_ap: x f y,
rel_exp: R^n,
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
ses-axioms: SecurityAxioms,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
noncelike-signatures: noncelike-signatures(s;es;thr),
ses-R: PropertyR,
ses-action: Action(e),
ses-used-atoms: UsedAtoms(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
true: True,
bfalse: ff,
bnot: ¬bb,
sq_type: SQType(T),
assert: ↑b,
ses-D: PropertyD,
ses-info-flow: ->>,
event-has*: e has* a,
rel_star: R^*,
ses-nonce-disjoint: NoncesCiphersAndKeysDisjoint,
event-has: (e has a),
class-value-has: X(e) has a,
ses-sig: signature(e),
pi2: snd(t),
same-action: same-action(x;y),
nat_plus: ℕ+
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:
2016_05_17-PM-00_36_34
Last ObjectModification:
2016_01_18-AM-07_52_29
Theory : event-logic-applications
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