{ 
[Info:Type]. [es:EO+(Info)]. [A:Type]. [X:EClass(A)]. [size:
].
[num:A 
]. [P:A 
]. [e:E].
Collect(size v's from X with maximum num[v] such that P[v])(e) = num[X(e)]
supposing 
e 
Collect(size v's from X with maximum num[v]
such that P[v]) }
{ Proof }
Definitions occuring in Statement :
es-collect-filter: Collect(size v's from X with maximum num[v] such that P[v]),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: b,
bool: ,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
universe: Type,
equal: s = t
Definitions :
outl: outl(x),
eq_bool: p =b q,
lt_int: i <z j,
le_int: i 
z j,
null: null(as),
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_str: Error :eq_str,
eq_id: a = b,
eq_lnk: a = b,
es-eq-E: e = e',
bimplies: p 
q,
eq_knd: a = b,
unit: Unit,
int_eq: if a=b then c else d,
minus: -n,
collect_accum: collect_accum(x.num[x];init;a,v.f[a; v];a.P[a]),
es-interface-accum: es-interface-accum(f;x;X),
collect_filter: collect_filter(),
bfalse: ff,
fpf-dom: x dom(f),
mapfilter: mapfilter(f;P;L),
list_accum: list_accum(x,a.f[x; a];y;l),
suptype: suptype(S; T),
squash: 
T,
do-apply: do-apply(f;x),
pi2: snd(t),
bnot: 
b,
pi1: fst(t),
bor: p 
q,
add: n + m,
it: 
,
inr: inr x ,
inl: inl x ,
spreadn: spread3,
es-filter-image: f[X],
natural_number: $n,
spread: spread def,
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
rev_implies: P 
Q,
exists: x:A. B[x],
btrue: tt,
atom_eq: atomeqn def,
sqequal: s ~ t,
or: P Q,
append: as @ bs,
locl: locl(a),
Knd: Knd,
atom: Atom$n,
isl: isl(x),
can-apply: can-apply(f;x),
list: type List,
guard: {T},
sq_type: SQType(T),
true: True,
int_nzero: 
,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
false: False,
not: A,
intensional-universe: IType,
fpf: a:A fp-> B[a],
record: record(x.T[x]),
real: 
,
grp_car: |g|,
l_member: (x l),
limited-type: LimitedType,
Id: Id,
es-interface-predecessors: (X)(e),
eq_int: (i =
j),
band: p 
q,
filter: filter(P;l),
length: ||as||,
es-loc: loc(e),
cand: A c B,
uiff: uiff(P;Q),
es-first-at: e is first@ i s.t. e.P[e],
le: A B,
alle-lt: e<e'.P[e],
implies: P Q,
product: x:A 
B[x],
and: P Q,
iff: P Q,
pair: <a, b>,
void: Void,
subtype: S 
T,
atom: Atom,
es-base-E: es-base-E(es),
token: "$token",
lambda: 
x.A[x],
es-E-interface: E(X),
subtype_rel: A r B,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
less_than: a < b,
int: ,
top: Top,
so_lambda: 
x.t[x],
all: x:A. B[x],
dep-isect: Error :dep-isect,
eq_atom: x =a y,
eq_atom: eq_atom$n(x;y),
record+: record+,
union: left + right,
set: {x:A| B[x]} ,
record-select: r.x,
axiom: Ax,
apply: f a,
so_apply: x[s],
es-collect-filter: Collect(size v's from X with maximum num[v] such that P[v]),
eclass-val: X(e),
prop: 
,
event_ordering: EO,
es-E: E,
bool: ,
uimplies: b supposing a,
equal: s = t,
event-ordering+: EO+(Info),
universe: Type,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
nat_plus: ,
uall: [x:A]. B[x],
member: t T,
isect: 
x:A. B[x],
function: x:A B[x],
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
RepUR: Error :RepUR,
CollapseTHENA: Error :CollapseTHENA,
nat: ,
THENM: Error :THENM,
in-eclass: e X,
assert: b,
AssertBY: Error :AssertBY
Lemmas :
es-E_wf,
top_wf,
nat_wf,
subtype_rel_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-collect-filter_wf,
es-interface-subtype_rel2,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
assert_wf,
bool_wf,
nat_plus_wf,
le_wf,
alle-lt_wf,
es-first-at_wf,
iff_weakening_uiff,
is-collect-filter,
Id_wf,
es-loc_wf,
es-interface-predecessors_wf,
es-E-interface_wf,
filter_wf,
length_wf1,
band_wf,
eq_int_wf,
eclass-val_wf,
intensional-universe_wf,
false_wf,
ifthenelse_wf,
true_wf,
length_wf_nat,
list-subtype,
l_member_wf,
filter_type,
uiff_inversion,
assert-eq-id,
subtype_base_sq,
bool_subtype_base,
assert_elim,
nat_plus_properties,
btrue_wf,
es-collect-accum_wf,
es-filter-image-val2,
es-is-filter-image2,
bor_wf,
pi1_wf_top,
bnot_wf,
pi2_wf,
iff_wf,
rev_implies_wf,
squash_wf,
do-apply_wf,
can-apply_wf,
es-collect-accum-val,
mapfilter_wf,
list_accum_wf,
assert_functionality_wrt_uiff,
bfalse_wf,
unit_wf,
es-interface-val_wf2,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
isl_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
\mforall{}[e:E].
Collect(size v's from X with maximum num[v] such that P[v])(e) = num[X(e)]
supposing \muparrow{}e \mmember{}\msubb{} Collect(size v's from X with maximum num[v] such that P[v])
Date html generated:
2011_08_16-PM-06_09_53
Last ObjectModification:
2010_11_29-PM-05_10_44
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