Nuprl Lemma : cabal-theorem
∀s:SecurityTheory. ∀es:EO+(Info). ∀C:Id List.
∀ns:Atom1 List. (C is a cabal for ns ⇒ Only agents in C have atoms in ns) supposing (∀A∈C.Honest(A))
Proof
Definitions occuring in Statement :
sth-es: sth-es(s),
security-theory: SecurityTheory,
ses-cabal: cabal is a cabal for atms,
ses-secrecy: Only agents in As have atoms in secrets,
ses-honest: Honest(A),
ses-info: Info,
event-ordering+: EO+(Info),
Id: Id,
l_all: (∀x∈L.P[x]),
list: T List,
atom: Atom$n,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions :
!hyp_hide: x
Lemmas :
ses-honest_witness,
sth-es_wf,
select_wf,
Id_wf,
sq_stable__le,
int_seg_wf,
length_wf,
es-causl-swellfnd,
event-ordering+_subtype,
ses-info_wf,
less_than_transitivity1,
less_than_irreflexivity,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
l_exists_iff,
l_member_wf,
event-has_wf,
l_exists_wf,
equal_wf,
es-E_wf,
all_wf,
int_seg_subtype-nat,
es-loc_wf,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
add-zero,
add-mul-special,
zero-mul,
ses-cabal_wf,
list_wf,
l_all_wf2,
ses-honest_wf,
event-ordering+_wf,
security-theory_wf,
l_all_iff,
exists_wf,
or_wf,
assert_wf,
in-eclass_wf,
ses-new_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
equal-wf-base-T,
atom1_subtype_base,
eclass-val_wf,
ses-encrypt_wf,
sdata_wf,
encryption-key_wf,
ses-crypt_wf,
not_wf,
equal-wf-base,
es-E-interface_wf,
ses-send_wf,
ses-encryption-key_wf,
ses-public-key_wf,
equal-wf-T-base,
ses-flow-induction,
es-causle_wf,
ses-flow_wf,
subtype_base_sq,
atom2_subtype_base,
es-le-loc,
es-causle_weakening_eq,
es-causl_transitivity2,
es-causle_weakening,
ses-flow-has,
es-causle_weakening_locl,
es-le_weakening,
squash_wf,
true_wf,
iff_weakening_equal,
ses-decryption-key_wf,
and_wf,
ses-key-rel_wf,
decidable__l_member,
decidable__equal_Id,
assert_elim,
ses-decrypt_wf,
bool_wf,
bool_subtype_base,
class-value-has_wf,
ses-sign_wf,
ses-verify_wf,
ses-rcv_wf,
free-from-atom_wf,
free-from-atom-outr,
bfalse_wf,
btrue_neq_bfalse,
isl_wf,
free-from-atom-subtype,
subtype_rel_sum,
security-event-structure_wf,
le_antisymmetry_iff,
le-add-cancel2,
pi2_wf,
ses-flow-implies',
es-locl_wf,
es-le_wf,
sq_stable__assert,
ses-decrypted_wf,
ses-encrypted_wf,
ses-cipher_wf,
symmetric-key_wf,
es-causl_weakening,
es-causle_transitivity,
event-has_functionality,
member_wf,
ses-flow-causle
Latex:
\mforall{}s:SecurityTheory. \mforall{}es:EO+(Info). \mforall{}C:Id List.
\mforall{}ns:Atom1 List. (C is a cabal for ns {}\mRightarrow{} Only agents in C have atoms in ns)
supposing (\mforall{}A\mmember{}C.Honest(A))
Date html generated:
2015_07_23-PM-00_25_29
Last ObjectModification:
2015_02_04-PM-03_19_36
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