{ 
[Info:Type]. [es:EO+(Info)]. [A,B:Type]. [base:B]. [f:B 
A B].
[X:EClass(A)]. [size:
]. [num:A ]. [P:A 
]. [e:E].
Collect(size v's from X with maximum num[v] such that P[v]
initialze x:=base on each v set x:=f[x;v])(e)
= <num[X(e)]
, list_accum(w,v.f[w;v];
base;
mapfilter(
e.X(e);e'.(num[X(e')] =
num[X(e)]);
(X)(e)))
>
supposing 
e 
Collect(size v's from X with maximum num[v] such that P[v]
initialze x:=base on each v set x:=f[x;v]) }
{ Proof }
Definitions occuring in Statement :
es-collect-filter-accum: es-collect-filter-accum,
es-interface-predecessors: (X)(e),
eclass-val: X(e),
in-eclass: e X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
eq_int: (i = j),
assert: b,
bool: ,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
universe: Type,
equal: s = t,
mapfilter: mapfilter(f;P;L),
list_accum: list_accum(x,a.f[x; a];y;l)
Definitions :
implies: P 
Q,
pi1: fst(t),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
Id: Id,
list: type List,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
le: A B,
ge: i 
j ,
not: 
A,
and: P 
Q,
uiff: uiff(P;Q),
axiom: Ax,
es-interface-predecessors: (X)(e),
eq_int: (i = j),
mapfilter: mapfilter(f;P;L),
list_accum: list_accum(x,a.f[x; a];y;l),
pair: <a, b>,
eclass-val: X(e),
void: Void,
es-E-interface: E(X),
less_than: a < b,
int: 
,
so_apply: x[s],
product: x:A B[x],
so_apply: x[s1;s2],
so_lambda: 
x.t[x],
es-collect-filter-accum: es-collect-filter-accum,
in-eclass: e X,
prop: 
,
assert: b,
uimplies: b supposing a,
bool: ,
set: {x:A| B[x]} ,
nat: ,
union: left + right,
nat_plus: ,
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,
event-ordering+: EO+(Info),
equal: s = t,
tactic: Error :tactic,
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_lnk: a = b,
es-eq-E: e = e',
bimplies: p q,
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(),
eq_knd: a = b,
fpf-dom: x dom(f),
bfalse: ff,
unit: Unit,
int_eq: if a=b then c else d,
eq_id: a = b,
suptype: suptype(S; T),
squash: 
T,
do-apply: do-apply(f;x),
spread: spread def,
pi2: snd(t),
bnot: b,
bor: p 
q,
add: n + m,
it: 
,
inr: inr x ,
inl: inl x ,
es-filter-image: f[X],
spreadn: spread4,
natural_number: $n,
spreadn: spread3,
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
rev_implies: P 
Q,
exists: x:A. B[x],
btrue: tt,
atom_eq: atomeqn def,
sqequal: s ~ t,
or: P Q,
append: as @ bs,
locl: locl(a),
Knd: Knd,
atom: Atom$n,
isl: isl(x),
can-apply: can-apply(f;x),
guard: {T},
sq_type: SQType(T),
true: True,
int_nzero: 
,
false: False,
intensional-universe: IType,
real: 
,
grp_car: |g|,
l_member: (x l),
limited-type: LimitedType,
band: p q,
filter: filter(P;l),
length: ||as||,
es-loc: loc(e),
cand: A c B,
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e],
iff: P Q,
CollapseTHEN: Error :CollapseTHEN,
MaAuto: Error :MaAuto,
RepUR: Error :RepUR,
RepeatFor: Error :RepeatFor,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
THENM: Error :THENM,
AssertBY: Error :AssertBY,
nil: [],
p-outcome: Outcome,
rationals: 
,
list_accum_pair: list_accum_pair(a,x.f[a; x];b,x.g[b; x];a0;b0;L)
Lemmas :
product_subtype_base,
int_subtype_base,
set_subtype_base,
bl-all_wf,
list_accum_pair-sq,
length-as-accum,
bl-all-as-accum,
le_wf,
alle-lt_wf,
es-first-at_wf,
iff_weakening_uiff,
is-collect-filter-accum,
es-loc_wf,
filter_wf,
length_wf1,
band_wf,
eq_int_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,
bor_wf,
pi1_wf_top,
bnot_wf,
pi2_wf,
es-is-filter-image2,
iff_wf,
rev_implies_wf,
squash_wf,
do-apply_wf,
can-apply_wf,
es-collect-accum-val,
bfalse_wf,
unit_wf,
es-interface-val_wf2,
assert_functionality_wrt_uiff,
es-interface-val_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
isl_wf,
Id_wf,
es-interface-predecessors_wf,
eclass-val_wf,
es-collect-filter-accum_wf,
nat_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-E_wf,
top_wf,
subtype_rel_wf,
es-interface-subtype_rel2,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
assert_wf,
bool_wf,
nat_plus_wf,
es-E-interface_wf,
mapfilter_wf,
list_accum_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[base:B]. \mforall{}[f:B {}\mrightarrow{} A {}\mrightarrow{} B]. \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] initialze x:=base
on each v set x:=f[x;v])(e)
= <num[X(e)]
, list\_accum(w,v.f[w;v];base;mapfilter(\mlambda{}e.X(e);\mlambda{}e'.(num[X(e')] =\msubz{} num[X(e)]);\mleq{}(X)(e)))
>
supposing \muparrow{}e \mmember{}\msubb{} Collect(size v's from X with maximum num[v] such that P[v] initialze x:=base
on each v set x:=f[x;v])
Date html generated:
2011_08_16-PM-05_30_53
Last ObjectModification:
2010_11_15-PM-02_54_47
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