Nuprl Lemma : ses-cipher-unique
∀[s:SES]
∀[es:EO+(Info)]. ∀[a,b:E(Encrypt)].
Encrypt(a) = Encrypt(b) ∈ (SecurityData × Key × Atom1) supposing cipherText(a) = cipherText(b) ∈ Atom1
supposing PropertyO
Proof
Definitions occuring in Statement :
ses-ordering: PropertyO,
ses-crypt: cipherText(e),
ses-encrypt: Encrypt,
ses-info: Info,
security-event-structure: SES,
encryption-key: Key,
sdata: SecurityData,
es-E-interface: E(X),
eclass-val: X(e),
event-ordering+: EO+(Info),
atom: Atom$n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
equal: s = t ∈ T
Lemmas :
equal_wf,
ses-crypt_wf,
es-E-interface_wf,
ses-encrypt_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
sdata_wf,
encryption-key_wf,
event-ordering+_wf,
ses-info_wf,
ses-ordering_wf,
security-event-structure_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
free-from-atom_wf,
eclass-val_wf,
or_wf,
assert_wf,
ses-decrypt_wf,
not_wf,
ses-sign_wf,
Id_wf,
ses-verify_wf,
ses-rcv_wf,
ses-send_wf,
ses-new_wf,
free-from-atom-pair-iff,
ses-encrypted_wf,
ses-encryption-key_wf,
atom1_subtype_base,
es-causle_weakening_locl,
es-causl_transitivity2,
es-causl_weakening,
es-causle_weakening,
product_subtype_base,
sdata_subtype_base,
union_subtype_base,
atom2_subtype_base
Latex:
\mforall{}[s:SES]
\mforall{}[es:EO+(Info)]. \mforall{}[a,b:E(Encrypt)].
Encrypt(a) = Encrypt(b) supposing cipherText(a) = cipherText(b)
supposing PropertyO
Date html generated:
2015_07_23-PM-00_07_04
Last ObjectModification:
2015_01_29-AM-07_53_23
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