Nuprl Lemma : ses-act-has-atom
∀s:SES
(ActionsDisjoint ⇒ (∀es:EO+(Info). ∀e:Act. ∀a:Atom1. ((e has a) ⇐⇒ (a ∈ UseableAtoms(e)) ∨ (a ∈ UsedAtoms(e)))))
Proof
Definitions occuring in Statement :
ses-useable-atoms: UseableAtoms(e),
ses-used-atoms: UsedAtoms(e),
ses-disjoint: ActionsDisjoint,
event-has: (e has a),
ses-act: Act,
ses-info: Info,
security-event-structure: SES,
event-ordering+: EO+(Info),
l_member: (x ∈ l),
atom: Atom$n,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q
Lemmas :
sq_stable_from_decidable,
ses-action_wf,
decidable__ses-action,
subtype_base_sq,
int_subtype_base,
ses-act_wf,
event-ordering+_wf,
ses-info_wf,
ses-disjoint_wf,
security-event-structure_wf,
in-eclass_wf,
ses-rcv_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
sdata_wf,
bool_wf,
not_wf,
less_than_wf,
false_wf,
equal-wf-base,
equal-wf-T-base,
assert_wf,
bnot_wf,
ses-sign_wf,
Id_wf,
ses-encrypt_wf,
encryption-key_wf,
ses-decrypt_wf,
ses-new_wf,
ses-send_wf,
ses-verify_wf,
member_singleton,
nil_member,
l_member_wf,
cons_wf,
eclass-val_wf,
nil_wf,
equal-wf-base-T,
atom1_subtype_base,
iff_wf,
or_wf,
true_wf,
free-from-atom_wf,
sdata-atoms_wf,
ses-crypt_wf,
append_wf,
ses-encrypted_wf,
encryption-key-atoms_wf,
ses-encryption-key_wf,
ses-decrypted_wf,
ses-cipher_wf,
ses-decryption-key_wf,
ses-sig_wf,
ses-signed_wf,
ses-verify-sig_wf,
ses-verify-signed_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
and_wf,
decidable__atom_equal_1,
free-from-atom-atom,
sdata-has-atom,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
free-from-atom-pair-iff,
decidable__l_member,
member_append,
encryption-key-free-from-atom,
sdata-free-from-atom,
cons_member,
ses-signer_wf,
free-from-atom-Id-rw,
ses-verify-signer_wf
Latex:
\mforall{}s:SES
(ActionsDisjoint
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}e:Act. \mforall{}a:Atom1. ((e has a) \mLeftarrow{}{}\mRightarrow{} (a \mmember{} UseableAtoms(e)) \mvee{} (a \mmember{} UsedAtoms(e)))))
Date html generated:
2015_07_23-PM-00_10_59
Last ObjectModification:
2015_01_29-AM-07_54_28
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