Nuprl Lemma : ses-flow-implies'
∀s:SES. ∀es:EO+(Info).
∀[P:E ─→ E ─→ Atom1 ─→ ℙ]
((∀e1,e2:E. ∀a:Atom1. (((e1 has a) ∧ (e2 has a) ∧ e1 ≤loc e2 ) ⇒ P[e1;e2;a]))
⇒ (∀e1,e2:E. ∀snd:E(Send). ∀rcv:E(Rcv). ∀a:Atom1.
((e1 c≤ snd
∧ rcv c≤ e2
∧ (snd < rcv)
∧ (Send(snd) = Rcv(rcv) ∈ SecurityData)
∧ (P[e1;snd;a] ∧ ses-flow(s;es;a;e1;snd))
∧ P[rcv;e2;a]
∧ ses-flow(s;es;a;rcv;e2))
⇒ P[e1;e2;a]))
⇒ (∀e1,e2:E. ∀encr:E(Encrypt). ∀decr:E(Decrypt). ∀a:Atom1.
(((e1 <loc encr)
∧ decr c≤ e2
∧ (encr < decr)
∧ ((plainText(decr) = plainText(encr) ∈ SecurityData)
∧ (cipherText(decr) = cipherText(encr) ∈ Atom1)
∧ MatchingKeys(key(decr);key(encr)))
∧ (¬(key(decr) = symmetric-key(a) ∈ Key))
∧ (P[e1;encr;a] ∧ ses-flow(s;es;a;e1;encr))
∧ (P[encr;decr;cipherText(encr)] ∧ ses-flow(s;es;cipherText(encr);encr;decr))
∧ P[decr;e2;a]
∧ ses-flow(s;es;a;decr;e2))
⇒ P[e1;e2;a]))
⇒ {∀e1,e2:E. ∀a:Atom1. (ses-flow(s;es;a;e1;e2) ⇒ P[e1;e2;a])})
Proof
Definitions occuring in Statement :
ses-flow: ses-flow(s;es;a;e1;e2),
event-has: (e has a),
ses-key-rel: MatchingKeys(k1;k2),
ses-cipher: cipherText(e),
ses-decryption-key: key(e),
ses-decrypted: plainText(e),
ses-decrypt: Decrypt,
ses-crypt: cipherText(e),
ses-encryption-key: key(e),
ses-encrypted: plainText(e),
ses-encrypt: Encrypt,
ses-rcv: Rcv,
ses-send: Send,
ses-info: Info,
security-event-structure: SES,
symmetric-key: symmetric-key(a),
encryption-key: Key,
sdata: SecurityData,
es-E-interface: E(X),
eclass-val: X(e),
event-ordering+: EO+(Info),
es-causle: e c≤ e',
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-causl: (e < e'),
es-E: E,
atom: Atom$n,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
ses-flow-induction,
ses-flow_wf,
all_wf,
es-causle_wf,
or_wf,
es-causl_wf,
es-E_wf,
event-ordering+_subtype,
ses-info_wf,
es-E-interface_wf,
ses-encrypt_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
subtype_top,
sdata_wf,
encryption-key_wf,
ses-decrypt_wf,
es-locl_wf,
ses-decrypted_wf,
ses-encrypted_wf,
ses-cipher_wf,
ses-crypt_wf,
ses-key-rel_wf,
ses-decryption-key_wf,
ses-encryption-key_wf,
not_wf,
equal-wf-T-base,
atom1_subtype_base,
ses-send_wf,
ses-rcv_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
event-has_wf,
es-le_wf,
security-event-structure_wf,
es-causle_weakening_eq,
es-causl_transitivity2,
es-causle_weakening,
es-causl_transitivity1,
es-causle_weakening_locl,
es-le_weakening,
es-causl_weakening
Latex:
\mforall{}s:SES. \mforall{}es:EO+(Info).
\mforall{}[P:E {}\mrightarrow{} E {}\mrightarrow{} Atom1 {}\mrightarrow{} \mBbbP{}]
((\mforall{}e1,e2:E. \mforall{}a:Atom1. (((e1 has a) \mwedge{} (e2 has a) \mwedge{} e1 \mleq{}loc e2 ) {}\mRightarrow{} P[e1;e2;a]))
{}\mRightarrow{} (\mforall{}e1,e2:E. \mforall{}snd:E(Send). \mforall{}rcv:E(Rcv). \mforall{}a:Atom1.
((e1 c\mleq{} snd
\mwedge{} rcv c\mleq{} e2
\mwedge{} (snd < rcv)
\mwedge{} (Send(snd) = Rcv(rcv))
\mwedge{} (P[e1;snd;a] \mwedge{} ses-flow(s;es;a;e1;snd))
\mwedge{} P[rcv;e2;a]
\mwedge{} ses-flow(s;es;a;rcv;e2))
{}\mRightarrow{} P[e1;e2;a]))
{}\mRightarrow{} (\mforall{}e1,e2:E. \mforall{}encr:E(Encrypt). \mforall{}decr:E(Decrypt). \mforall{}a:Atom1.
(((e1 <loc encr)
\mwedge{} decr c\mleq{} e2
\mwedge{} (encr < decr)
\mwedge{} ((plainText(decr) = plainText(encr))
\mwedge{} (cipherText(decr) = cipherText(encr))
\mwedge{} MatchingKeys(key(decr);key(encr)))
\mwedge{} (\mneg{}(key(decr) = symmetric-key(a)))
\mwedge{} (P[e1;encr;a] \mwedge{} ses-flow(s;es;a;e1;encr))
\mwedge{} (P[encr;decr;cipherText(encr)] \mwedge{} ses-flow(s;es;cipherText(encr);encr;decr))
\mwedge{} P[decr;e2;a]
\mwedge{} ses-flow(s;es;a;decr;e2))
{}\mRightarrow{} P[e1;e2;a]))
{}\mRightarrow{} \{\mforall{}e1,e2:E. \mforall{}a:Atom1. (ses-flow(s;es;a;e1;e2) {}\mRightarrow{} P[e1;e2;a])\})
Date html generated:
2015_07_23-PM-00_05_12
Last ObjectModification:
2015_01_29-AM-07_49_09
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