Nuprl Lemma : encryption-key-free-from-atom
∀[k:Key]. ∀[a:Atom1]. uiff(¬(a ∈ encryption-key-atoms(k));a#k:Key)
Proof
Definitions occuring in Statement :
encryption-key-atoms: encryption-key-atoms(k),
encryption-key: Key,
l_member: (x ∈ l),
free-from-atom: a#x:T,
atom: Atom$n,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
encryption-key: Key,
encryption-key-atoms: encryption-key-atoms(k),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
false: False,
sq_type: SQType(T),
guard: {T},
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
outr: outr(x),
btrue: tt,
true: True,
outl: outl(x)
Latex:
\mforall{}[k:Key]. \mforall{}[a:Atom1]. uiff(\mneg{}(a \mmember{} encryption-key-atoms(k));a\#k:Key)
Date html generated:
2016_05_17-AM-11_40_47
Last ObjectModification:
2015_12_29-PM-06_45_31
Theory : event-logic-applications
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