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
Lemmas :
sq_stable_from_decidable,
ses-action_wf,
decidable__ses-action,
ses-act-has-atom,
equal-wf-base-T,
atom1_subtype_base,
ses-private_wf,
exists_wf,
es-locl_wf,
event-has_wf,
ses-thread-member_wf,
ses-act_wf,
ses-legal-thread_wf,
ses-thread_wf,
Id_wf,
event-ordering+_wf,
ses-info_wf,
ses-disjoint_wf,
security-event-structure_wf,
decidable__atom_equal_1,
l_member_wf,
ses-useable-atoms_wf,
event-ordering+_subtype,
or_wf,
ses-thread-order,
l_all_iff,
ses-used-atoms_wf,
select_wf,
sq_stable__le,
cons_wf,
concat_wf,
map_wf,
le_wf,
less_than_wf,
list_wf,
less_than_transitivity2,
length_wf,
le_weakening2,
from-upto_wf,
squash_wf,
true_wf,
es-E_wf,
iff_weakening_equal,
cons_member,
member-concat,
member_map,
lelt_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
decidable__lt,
less-iff-le,
add-swap,
all_wf,
int_seg_wf,
subtract_wf,
le-add-cancel2,
equal_wf
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:
2015_07_23-PM-00_11_14
Last ObjectModification:
2015_02_04-PM-03_37_53
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