Nuprl Lemma : member-used-atoms
∀s:SES
(ActionsDisjoint
⇒ (∀es:EO+(Info). ∀e:E. ∀a:Atom1.
((a ∈ UsedAtoms(e))
⇐⇒ ((↑e ∈b Send) ∧ (a ∈ sdata-atoms(Send(e))))
∨ ((↑e ∈b Decrypt) ∧ ((a = cipherText(e) ∈ Atom1) ∨ (a ∈ encryption-key-atoms(key(e)))))
∨ ((↑e ∈b Verify) ∧ ((a = signature(e) ∈ Atom1) ∨ (a ∈ sdata-atoms(signed(e)))))
∨ ((↑e ∈b Sign) ∧ (a ∈ sdata-atoms(signed(e))))
∨ ((↑e ∈b Encrypt) ∧ ((a ∈ sdata-atoms(plainText(e))) ∨ (a ∈ encryption-key-atoms(key(e))))))))
Proof
Definitions occuring in Statement :
ses-used-atoms: UsedAtoms(e),
ses-disjoint: ActionsDisjoint,
ses-cipher: cipherText(e),
ses-decryption-key: key(e),
ses-decrypt: Decrypt,
ses-encryption-key: key(e),
ses-encrypted: plainText(e),
ses-encrypt: Encrypt,
ses-verify-sig: signature(e),
ses-verify-signed: signed(e),
ses-verify: Verify,
ses-signed: signed(e),
ses-sign: Sign,
ses-send: Send,
ses-info: Info,
security-event-structure: SES,
encryption-key-atoms: encryption-key-atoms(k),
sdata-atoms: sdata-atoms(d),
eclass-val: X(e),
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-E: E,
l_member: (x ∈ l),
atom: Atom$n,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
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-used-atoms: UsedAtoms(e),
ses-disjoint: ActionsDisjoint,
member: t ∈ T,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
assert: ↑b,
iff: P ⇐⇒ Q,
or: P ∨ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
es-E-interface: E(X),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb
Latex:
\mforall{}s:SES
(ActionsDisjoint
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}a:Atom1.
((a \mmember{} UsedAtoms(e))
\mLeftarrow{}{}\mRightarrow{} ((\muparrow{}e \mmember{}\msubb{} Send) \mwedge{} (a \mmember{} sdata-atoms(Send(e))))
\mvee{} ((\muparrow{}e \mmember{}\msubb{} Decrypt) \mwedge{} ((a = cipherText(e)) \mvee{} (a \mmember{} encryption-key-atoms(key(e)))))
\mvee{} ((\muparrow{}e \mmember{}\msubb{} Verify) \mwedge{} ((a = signature(e)) \mvee{} (a \mmember{} sdata-atoms(signed(e)))))
\mvee{} ((\muparrow{}e \mmember{}\msubb{} Sign) \mwedge{} (a \mmember{} sdata-atoms(signed(e))))
\mvee{} ((\muparrow{}e \mmember{}\msubb{} Encrypt)
\mwedge{} ((a \mmember{} sdata-atoms(plainText(e))) \mvee{} (a \mmember{} encryption-key-atoms(key(e))))))))
Date html generated:
2016_05_17-PM-00_31_47
Last ObjectModification:
2016_01_18-AM-07_43_11
Theory : event-logic-applications
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