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 unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
l_all: (∀x∈L.P[x]),
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
security-theory: SecurityTheory,
sth-es: sth-es(s),
pi1: fst(t),
ses-cabal: cabal is a cabal for atms,
ses-secrecy: Only agents in As have atoms in secrets,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
ses-axioms: SecurityAxioms,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-E-interface: E(X),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
ses-flow: ses-flow(s;es;a;e1;e2),
ycomb: Y,
Id: Id,
sq_type: SQType(T),
ses-S: PropertyS,
true: True,
rev_implies: P ⇐ Q,
ses-K: PropertyK,
sym: Sym(T;x,y.E[x; y]),
event-has: (e has a),
class-value-has: X(e) has a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
ses-decryption-key: key(e),
symmetric-key: symmetric-key(a),
encryption-key: Key,
isl: isl(x),
outr: outr(x),
ses-flow-axiom: PropertyF,
cand: A c∧ B,
ses-disjoint: ActionsDisjoint,
ses-crypt: cipherText(e),
es-le: e ≤loc e' ,
sq_stable: SqStable(P),
es-locl: (e <loc e'),
same-action: same-action(x;y)
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:
2016_05_17-PM-00_52_52
Last ObjectModification:
2016_01_18-AM-07_50_41
Theory : event-logic-applications
Home
Index