{ 
[Info,A:Type]. [F:Id 
dataflow(Info;bag(A))]. [es:EO+(Info)]. [e:E].
(Prior(dataflow-set-class(x.F[x])) es e
~ if null(filter(
x.0 <z bag-size(x);
data-stream(F[loc(e)];map(e.info(e);before(e)))))
then {}
else last(filter(x.0 <z bag-size(x);
data-stream(F[loc(e)];map(e.info(e);before(e)))))
fi ) }
{ Proof }
Definitions occuring in Statement :
dataflow-set-class: dataflow-set-class(x.P[x]),
primed-class: Prior(X),
es-info: info(e),
event-ordering+: EO+(Info),
es-before: before(e),
es-loc: loc(e),
es-E: E,
data-stream: data-stream(P;L),
dataflow: dataflow(A;B),
Id: Id,
map: map(f;as),
null: null(as),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
uall: [x:A]. B[x],
so_apply: x[s],
apply: f a,
lambda: x.A[x],
function: x:A B[x],
natural_number: $n,
universe: Type,
sqequal: s ~ t,
filter: filter(P;l),
last: last(L),
bag-size: bag-size(bs),
empty-bag: {},
bag: bag(T)
Definitions :
l_member: (x 
l),
rcv: rcv(l,tg),
locl: locl(a),
Knd: Knd,
dataflow-ap: df(a),
pi2: snd(t),
listp: A List
,
combination: Combination(n;T),
iterate-dataflow: P*(inputs),
es-le-before: 
loc(e),
qabs: |r|,
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-p-le: e p e',
es-causle: e c e',
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
record: record(x.T[x]),
nil: [],
cons: [car / cdr],
append: as @ bs,
tl: tl(l),
hd: hd(l),
quotient: x,y:A//B[x; y],
sq_type: SQType(T),
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
bfalse: ff,
btrue: tt,
eq_bool: p =b q,
le_int: i z j,
eq_int: (i =
j),
set_blt: a <
b,
grp_blt: a < b,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
es-bless: e <loc e',
es-ble: e loc e',
bimplies: p 
q,
band: p 
q,
bor: p 
q,
es-first: first(e),
bnot: 
b,
unit: Unit,
bool: 
,
isect2: T1 
T2,
b-union: A 
B,
union: left + right,
fpf-sub: f 
g,
deq: EqDecider(T),
ma-state: State(ds),
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
fpf-dom: x dom(f),
guard: {T},
pair: <a, b>,
class-program: ClassProgram(T),
fpf-cap: f(x)?z,
strong-subtype: strong-subtype(A;B),
and: P Q,
uiff: uiff(P;Q),
fpf: a:A fp-> B[a],
es-E-interface: E(X),
uimplies: b supposing a,
subtype_rel: A r B,
eclass: EClass(A[eo; e]),
atom: Atom$n,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
corec: corec(T.F[T]),
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
assert: 
b,
record-select: r.x,
primed-class: Prior(X),
last: last(L),
empty-bag: {},
data-stream: data-stream(P;L),
bag-size: bag-size(bs),
lt_int: i <z j,
filter: filter(P;l),
null: null(as),
ifthenelse: if b then t else f fi ,
top: Top,
so_apply: x[s],
so_lambda: 
x.t[x],
dataflow-set-class: dataflow-set-class(x.P[x]),
true: True,
squash: 
T,
es-causl: (e < e'),
apply: f a,
limited-type: LimitedType,
real: 
,
grp_car: |g|,
minus: -n,
add: n + m,
subtract: n - m,
void: Void,
false: False,
not: A,
natural_number: $n,
prop: 
,
le: A B,
ge: i 
j ,
int: 
,
set: {x:A| B[x]} ,
less_than: a < b,
nat: 
,
implies: P Q,
product: x:A 
B[x],
exists: x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
subtype: S T,
all: x:A. B[x],
universe: Type,
dataflow: dataflow(A;B),
bag: bag(T),
Id: Id,
function: x:A B[x],
event-ordering+: EO+(Info),
event_ordering: EO,
es-E: E,
member: t T,
isect: x:A. B[x],
uall: [x:A]. B[x],
es-pred: pred(e),
es-before: before(e),
es-info: info(e),
lambda: x.A[x],
map: map(f;as),
list: type List,
equal: s = t,
es-loc: loc(e),
sqequal: s ~ t
Lemmas :
assert_of_null,
not_functionality_wrt_uiff,
append_wf,
null_wf3,
append_is_nil,
nat_wf,
es-E_wf,
ge_wf,
nat_properties,
es-causl-swellfnd,
bag_wf,
dataflow_wf,
Id_wf,
event-ordering+_wf,
event-ordering+_inc,
le_wf,
member_wf,
es-causl_wf,
dataflow-set-class_wf,
primed-class-cases,
top_wf,
subtype_rel_wf,
true_wf,
squash_wf,
es-base-E_wf,
subtype_rel_self,
dataflow_subtype,
subtype_rel_bag,
bool_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
bnot_wf,
es-first_wf,
primed-class_wf,
ifthenelse_wf,
subtype_base_sq,
lt_int_wf,
bool_subtype_base,
null_wf,
es-pred_wf,
es-pred-causl,
data-stream_wf,
filter_wf,
last_wf,
dataflow-history-val_wf,
es-loc_wf,
atom2_subtype_base,
es-loc-pred,
es-info_wf,
es-before_wf,
map_wf,
iterate-dataflow_wf,
map_append_sq,
data-stream-append,
filter_append,
es-before_wf3,
es-locl_wf,
bag-size_wf,
data-stream-cons,
last_append,
subtype_rel_list,
false_wf,
dataflow-ap_wf,
pi2_wf,
last-cons,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
le_int_wf,
list_subtype_base,
append-nil,
filter_wf_top,
l_member_wf
\mforall{}[Info,A:Type]. \mforall{}[F:Id {}\mrightarrow{} dataflow(Info;bag(A))]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(Prior(dataflow-set-class(x.F[x])) es e
\msim{} if null(filter(\mlambda{}x.0 <z bag-size(x);data-stream(F[loc(e)];map(\mlambda{}e.info(e);before(e)))))
then \{\}
else last(filter(\mlambda{}x.0 <z bag-size(x);data-stream(F[loc(e)];map(\mlambda{}e.info(e);before(e)))))
fi )
Date html generated:
2011_08_16-PM-06_13_20
Last ObjectModification:
2011_06_20-AM-01_50_46
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