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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
ses-used-atoms: UsedAtoms(e),
ses-useable-atoms: UseableAtoms(e),
event-has: (e has a),
class-value-has: X(e) has a,
ses-disjoint: ActionsDisjoint,
member: t ∈ T,
exists: ∃x:A. B[x],
ses-act: Act,
uall: ∀[x:A]. B[x],
sq_stable: SqStable(P),
squash: ↓T,
and: P ∧ Q,
cand: A c∧ B,
ses-action: Action(e),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
false: False,
true: True,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
es-E-interface: E(X),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
decidable: Dec(P),
bnot: ¬bb,
ses-crypt: cipherText(e),
ses-encryption-key: key(e),
ses-encrypted: plainText(e),
pi1: fst(t),
pi2: snd(t),
rev_uimplies: rev_uimplies(P;Q),
ses-cipher: cipherText(e),
ses-decryption-key: key(e),
ses-decrypted: plainText(e),
ses-sig: signature(e),
ses-signer: signer(e),
ses-signed: signed(e),
ses-verify-sig: signature(e),
ses-verify-signer: signer(e),
ses-verify-signed: signed(e)
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:
2016_05_17-PM-00_32_34
Last ObjectModification:
2016_01_18-AM-07_51_55
Theory : event-logic-applications
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