{ 
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)))))))) }
{ 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,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
or: P Q,
and: P Q,
equal: s = t,
l_member: (x l),
atom: Atom$n
Definitions :
member: t T,
ses-thread: Thread,
Id: Id,
ses-legal-thread: Legal(thr)@A,
atom: Atom$n,
ses-act: Act,
ses-thread-member: e thr,
event-has: (e has a),
l_member: (x l),
not: 
A,
ses-disjoint: ActionsDisjoint,
security-event-structure: SES,
event-ordering+: EO+(Info),
equal: s = t,
function: x:A 
B[x],
all: x:A. B[x],
ses-private: Private(A),
prop: 
,
universe: Type,
limited-type: LimitedType,
es-E: E,
set: {x:A| B[x]} ,
ses-useable-atoms: UseableAtoms(e),
union: left + right,
or: P Q,
product: x:A 
B[x],
false: False,
implies: P Q,
and: P Q,
assert: 
b,
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
l_all: (xL.P[x]),
l_contains: A 
B,
exists: x:A. B[x],
class-value-has: X(e) has a,
less_than: a < b,
void: Void,
ses-info: Info,
ses-used-atoms: UsedAtoms(e),
bool: 
,
es-locl: (e <loc e'),
subtype_rel: A r B,
strong-subtype: strong-subtype(A;B),
event_ordering: EO,
eclass-val: X(e),
alle-between3: e(e1,e2].P[e],
es-pred: pred(e),
es-causl: (e < e'),
cand: A c B,
int_seg: {i..j
},
nat: 
,
subtype: S T,
top: Top,
token: "$token",
ifthenelse: if b then t else f fi ,
atom: Atom,
apply: f a,
record-select: r.x,
guard: {T},
decidable: Dec(P),
rationals: 
,
qle: r 
s,
qless: r < s,
q-rel: q-rel(r;x),
p-outcome: Outcome,
dstype: dstype(TypeNames; d; a),
fset-member: a s,
f-subset: xs ys,
fset: FSet{T},
fset-closed: (s closed under fs),
string: Error :string,
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
consensus-rcv: consensus-rcv(V;A),
infix_ap: x f y,
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-E-interface: E(X),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (xL. P[x]),
fun-connected: y is f*(x),
iff: P 
Q,
le: A B,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
list: type List,
unit: Unit,
rev_implies: P Q,
true: True,
sq_stable: SqStable(P),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
fpf-sub: f g,
MaAuto: Error :MaAuto,
D: Error :D,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
ses-action: Action(e),
AssertBY: Error :AssertBY,
pair: <a, b>,
ParallelOp: Error :ParallelOp,
Unfold: Error :Unfold,
select: l[i],
length: ||as||,
int: 
,
lelt: i j < k,
natural_number: $n,
real: 
,
from-upto: [n, m),
lambda: 
x.A[x],
listp: A List
,
combination: Combination(n;T),
map: map(f;as),
concat: concat(ll),
add: n + m,
minus: -n,
subtract: n - m,
nil: [],
cons: [car / cdr],
ge: i 
j ,
es-loc: loc(e),
sqequal: s ~ t,
sq_type: SQType(T),
isect: 
x:A. B[x]
Lemmas :
top_wf,
non_neg_length,
nat_wf,
cons_one_one,
atom_sq,
atom1_sq,
guard_wf,
length_wf_nat,
int_seg_wf,
int_seg_properties,
member_map,
member-concat,
ses-used-atoms_wf,
cons_member,
concat_wf,
map_wf,
le_wf,
select_wf,
from-upto_wf,
length_wf1,
not_wf,
false_wf,
ses-thread-order,
member_wf,
ses-legal-thread_wf,
ses-thread_wf,
event-ordering+_wf,
ses-disjoint_wf,
security-event-structure_wf,
sq_stable_from_decidable,
decidable__ses-action,
ses-action_wf,
ses-act-has-atom,
decidable__or,
decidable__l_member,
decidable__atom_equal_1,
es-E_wf,
subtype_rel_self,
event-ordering+_inc,
ses-info_wf,
ses-act_wf,
ses-thread-member_wf,
event-has_wf,
es-causl_wf,
Id_wf,
es-locl_wf,
l_member_wf,
ses-useable-atoms_wf,
ses-private_wf
\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:
2011_08_17-PM-07_35_50
Last ObjectModification:
2010_09_24-PM-02_42_18
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