Nuprl Lemma : ses-legal-thread-decrypt
∀s:SES
(ActionsDisjoint
⇒ PropertyD
⇒ (∀es:EO+(Info). ∀A:Id. ∀thr:Thread. ∀e:E.
(Legal(thr)@A
⇒ e ∈ thr ⇒ (∃a:Act. ((a <loc e) ∧ a ∈ thr ∧ (a has cipherText(e)))) supposing ↑e ∈b Decrypt))
supposing NoncesCiphersAndKeysDisjoint)
Proof
Definitions occuring in Statement :
ses-legal-thread: Legal(thr)@A,
ses-thread-member: e ∈ thr,
ses-thread: Thread,
ses-nonce-disjoint: NoncesCiphersAndKeysDisjoint,
ses-disjoint: ActionsDisjoint,
ses-D: PropertyD,
event-has: (e has a),
ses-act: Act,
ses-cipher: cipherText(e),
ses-decrypt: Decrypt,
ses-info: Info,
security-event-structure: SES,
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
ses-thread-member: e ∈ thr,
ses-legal-thread: Legal(thr)@A,
ses-thread: Thread,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
ses-nonce-disjoint: NoncesCiphersAndKeysDisjoint,
and: P ∧ Q,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
es-E-interface: E(X),
top: Top,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than: a < b,
squash: ↓T,
ses-act: Act,
so_apply: x[s],
uiff: uiff(P;Q),
l_contains: A ⊆ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
ses-D: PropertyD,
sq_stable: SqStable(P),
le: A ≤ B
Latex:
\mforall{}s:SES
(ActionsDisjoint
{}\mRightarrow{} PropertyD
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}A:Id. \mforall{}thr:Thread. \mforall{}e:E.
(Legal(thr)@A
{}\mRightarrow{} e \mmember{} thr {}\mRightarrow{} (\mexists{}a:Act. ((a <loc e) \mwedge{} a \mmember{} thr \mwedge{} (a has cipherText(e))))
supposing \muparrow{}e \mmember{}\msubb{} Decrypt))
supposing NoncesCiphersAndKeysDisjoint)
Date html generated:
2016_05_17-PM-00_33_18
Last ObjectModification:
2016_01_18-AM-07_44_24
Theory : event-logic-applications
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