Nuprl Lemma : ses-legal-thread-has-atom
∀s:SES
(ActionsDisjoint
⇒ (∀es:EO+(Info). ∀A:Id. ∀thr:Thread.
(Legal(thr)@A
⇒ (∀a:Atom1. ∀e:Act.
(e ∈ thr
⇒ (e has a)
⇒ ((∃e':Act. ((e' <loc e) ∧ (e' has a) ∧ e' ∈ thr))
∨ (a ∈ UseableAtoms(e))
∨ (a = Private(A) ∈ Atom1)))))))
Proof
Definitions occuring in Statement :
ses-legal-thread: Legal(thr)@A,
ses-useable-atoms: UseableAtoms(e),
ses-thread-member: e ∈ thr,
ses-thread: Thread,
ses-disjoint: ActionsDisjoint,
event-has: (e has a),
ses-act: Act,
ses-private: Private(A),
ses-info: Info,
security-event-structure: SES,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
Id: Id,
l_member: (x ∈ l),
atom: Atom$n,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
ses-act: Act,
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
squash: ↓T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
guard: {T},
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
decidable: Dec(P),
ses-thread-member: e ∈ thr,
exists: ∃x:A. B[x],
ses-thread: Thread,
ses-legal-thread: Legal(thr)@A,
l_contains: A ⊆ B,
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
less_than: a < b,
true: True,
rev_implies: P ⇐ Q,
le: A ≤ B,
cand: A c∧ B,
uiff: uiff(P;Q),
es-locl: (e <loc e')
Latex:
\mforall{}s:SES
(ActionsDisjoint
{}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}A:Id. \mforall{}thr:Thread.
(Legal(thr)@A
{}\mRightarrow{} (\mforall{}a:Atom1. \mforall{}e:Act.
(e \mmember{} thr
{}\mRightarrow{} (e has a)
{}\mRightarrow{} ((\mexists{}e':Act. ((e' <loc e) \mwedge{} (e' has a) \mwedge{} e' \mmember{} thr))
\mvee{} (a \mmember{} UseableAtoms(e))
\mvee{} (a = Private(A))))))))
Date html generated:
2016_05_17-PM-00_33_03
Last ObjectModification:
2016_01_18-AM-07_43_40
Theory : event-logic-applications
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