{ 
[Info:Type]. [es:EO+(Info)]. [T:Type]. [X:EClass(T)]. [P:E(X) 
].
[n:
]. [e:E]. [i:Id].
{(
e 
X) 
(P[e])}
supposing e is first@ i s.t. q.||filter(
e.P[e];
(X)(q))|| = n }
{ Proof }
Definitions occuring in Statement :
es-interface-predecessors: (X)(e),
es-E-interface: E(X),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first-at: e is first@ i s.t. e.P[e],
es-E: E,
Id: Id,
length: ||as||,
assert: b,
bool: ,
nat_plus: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
so_apply: x[s],
and: P Q,
lambda: x.A[x],
function: x:A B[x],
int: 
,
universe: Type,
equal: s = t,
filter: filter(P;l)
Definitions :
in-eclass: e X,
strong-subtype: strong-subtype(A;B),
alle-lt: e<e'.P[e],
le: A B,
ge: i 
j ,
not: 
A,
uiff: uiff(P;Q),
implies: P 
Q,
pair: <a, b>,
void: Void,
false: False,
true: True,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
guard: {T},
so_apply: x[s],
l_member: (x l),
product: x:A 
B[x],
and: P Q,
assert: b,
es-loc: loc(e),
less_than: a < b,
es-interface-predecessors: (X)(e),
filter: filter(P;l),
length: ||as||,
limited-type: LimitedType,
atom: Atom$n,
prop: 
,
int: ,
so_lambda: 
x.t[x],
es-first-at: e is first@ i s.t. e.P[e],
uimplies: b supposing a,
Id: Id,
set: {x:A| B[x]} ,
nat_plus: ,
union: left + right,
es-E-interface: E(X),
bool: ,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
all: x:A. B[x],
function: x:A B[x],
isect: 
x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
member: t T,
equal: s = t,
event-ordering+: EO+(Info),
tactic: Error :tactic,
eclass-val: X(e),
es-pred: pred(e),
IdLnk: IdLnk,
append: as @ bs,
locl: locl(a),
Knd: Knd,
cond-class: [X?Y],
eq_knd: a = b,
fpf-dom: x dom(f),
isl: isl(x),
can-apply: can-apply(f;x),
or: P 
Q,
divides: b | a,
assoced: a ~ b,
set_leq: a b,
set_lt: a <p b,
grp_lt: a < b,
l_contains: A B,
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (
xL. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
qle: r s,
qless: r < s,
q-rel: q-rel(r;x),
list: type List,
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
fset-member: a s,
f-subset: xs ys,
fset-closed: (s closed under fs),
l_disjoint: l_disjoint(T;l1;l2),
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-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
infix_ap: x f y,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.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),
unit: Unit,
exists: x:A. B[x],
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
decidable: Dec(P),
int_nzero: 
,
real: 
,
nat: ,
fpf: a:A fp-> B[a],
cand: A c B,
tl: tl(l),
hd: hd(l),
bfalse: ff,
eq_bool: p =b q,
lt_int: i <z j,
le_int: i z j,
eq_int: (i =
j),
null: null(as),
set_blt: a < b,
grp_blt: a < b,
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_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
bimplies: p q,
band: p q,
bor: p q,
bnot: b,
cons: [car / cdr],
nil: [],
btrue: tt,
es-prior-interface: prior(X),
sq_type: SQType(T),
iff: P 
Q,
rev_implies: P Q,
fpf-cap: f(x)?z,
sqequal: s ~ t,
es-le-before: loc(e),
eclass-events: eclass-events(es;X;L),
es-first: first(e),
lsrc: source(l),
ldst: destination(l),
es-init: es-init(es;e),
natural_number: $n,
grp_car: |g|,
select: l[i],
intensional-universe: IType,
fpf-sub: f g,
map-class: (f[v] where v from X),
deq: EqDecider(T),
ma-state: State(ds),
class-program: ClassProgram(T),
map: map(f;as)
Lemmas :
filter_wf_top,
append-nil,
subtype_rel_list,
intensional-universe_wf,
l_member_wf,
list-subtype,
list-set-type2,
nat_wf,
select_wf,
l_all_wf,
es-le-loc,
atom2_subtype_base,
es-le_wf,
int_subtype_base,
es-loc-pred,
false_wf,
set_subtype_base,
eclass-events_wf,
es-le-before_wf,
es-prior-interface-locl,
filter_append_sq,
eclass-val_wf,
eclass-val_wf2,
es-locl_irreflexivity,
es-interface-subtype_rel2,
es-prior-interface_wf,
top_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
iff_weakening_uiff,
bool_subtype_base,
subtype_base_sq,
eqtt_to_assert,
bool_cases,
es-interface-predecessors-general-step,
squash_wf,
true_wf,
rev_implies_wf,
iff_wf,
es-prior-interface_wf1,
bnot_wf,
subtype_rel_wf,
es-first-at-implies,
decidable_wf,
decidable__cand,
decidable__assert,
uiff_inversion,
not_wf,
length_wf_nat,
es-locl_wf,
es-causl_wf,
member_wf,
eclass_wf,
es-E-interface_wf,
Id_wf,
es-interface-top,
es-interface-predecessors_wf,
event-ordering+_inc,
subtype_rel_self,
es-E_wf,
es-loc_wf,
filter_wf,
length_wf1,
es-first-at_wf,
nat_plus_wf,
bool_wf,
event-ordering+_wf,
nat_plus_properties,
assert_witness,
assert_wf,
guard_wf,
in-eclass_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[P:E(X) {}\mrightarrow{} \mBbbB{}]. \mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[e:E]. \mforall{}[i:Id].
\{(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}P[e])\} supposing e is first@ i s.t. q.||filter(\mlambda{}e.P[e];\mleq{}(X)(q))|| = n
Date html generated:
2011_08_16-PM-05_24_20
Last ObjectModification:
2011_06_20-AM-01_23_04
Home
Index