Nuprl Lemma : ses-sign-has-atom
∀s:SES. ∀es:EO+(Info). ∀e:E. ∀a:Atom1.
(Sign(e) has a ⇐⇒ (↑e ∈b Sign) ∧ ((a = signature(e) ∈ Atom1) ∨ (a ∈ sdata-atoms(signed(e)))))
Proof
Definitions occuring in Statement :
ses-signed: signed(e),
ses-sig: signature(e),
ses-sign: Sign,
ses-info: Info,
security-event-structure: SES,
sdata-atoms: sdata-atoms(d),
sdata: SecurityData,
class-value-has: X(e) has a,
in-eclass: e ∈b X,
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
l_member: (x ∈ l),
atom: Atom$n,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
product: x:A × B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
ses-signed: signed(e),
ses-sig: signature(e),
class-value-has: X(e) has a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
implies: P ⇒ Q,
pi2: snd(t),
pi1: fst(t),
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
uiff: uiff(P;Q),
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
guard: {T}
Latex:
\mforall{}s:SES. \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}a:Atom1.
(Sign(e) has a \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} Sign) \mwedge{} ((a = signature(e)) \mvee{} (a \mmember{} sdata-atoms(signed(e)))))
Date html generated:
2016_05_17-AM-11_45_55
Last ObjectModification:
2015_12_29-PM-06_42_05
Theory : event-logic-applications
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