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
Lemmas :
in-eclass_wf,
ses-info_wf,
ses-send_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
sdata_wf,
bool_wf,
eqtt_to_assert,
l_member_wf,
sdata-atoms_wf,
eclass-val_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-commutes,
le-add-cancel2,
or_wf,
true_wf,
assert_wf,
ses-decrypt_wf,
encryption-key_wf,
equal-wf-base-T,
atom1_subtype_base,
ses-cipher_wf,
encryption-key-atoms_wf,
ses-decryption-key_wf,
ses-verify_wf,
Id_wf,
ses-verify-sig_wf,
ses-verify-signed_wf,
ses-sign_wf,
ses-signed_wf,
ses-encrypt_wf,
ses-encrypted_wf,
ses-encryption-key_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
cons_wf,
cons_member,
append_wf,
member_append,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
nil_wf,
ses-disjoint_wf,
security-event-structure_wf
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:
2015_07_23-PM-00_10_25
Last ObjectModification:
2015_01_29-AM-07_53_55
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