{ 
[Info,A:Type]. [X:EClass(A)]. [size:
]. [num:A 
]. [P:A 
].
(Collect(size v's from X with maximum num[v] such that P[v])
= collectfilterfun()[
es-interface-accum(collectfilteracc(size;v.num[v];v.P[v]);<-1, 0, inr 0 >;
X)]) }
{ Proof }
Definitions occuring in Statement :
collectfilterfun: collectfilterfun(),
collectfilteracc: collectfilteracc(size;v1.num[v1];v2.P[v2]),
es-collect-filter: Collect(size v's from X with maximum num[v] such that P[v]),
es-interface-accum: es-interface-accum(f;x;X),
es-filter-image: f[X],
eclass: EClass(A[eo; e]),
bool: ,
nat_plus: ,
nat: ,
uall: [x:A]. B[x],
so_apply: x[s],
function: x:A B[x],
pair: <a, b>,
inr: inr x ,
minus: -n,
natural_number: $n,
universe: Type,
equal: s = t
Definitions :
member: t 
T,
so_lambda: 
x y.t[x; y],
eclass: EClass(A[eo; e]),
es-filter-image: f[X],
collectfilterfun: collectfilterfun(),
es-interface-accum: es-interface-accum(f;x;X),
collectfilteracc: collectfilteracc(size;v1.num[v1];v2.P[v2]),
collectfilterfun2: collectfilterfun2(),
collectfilteracc2: collectfilteracc2(size;v1.num[v1];v2.P[v2]),
btrue: tt,
ifthenelse: if b then t else f fi ,
top: Top,
p-compose: f o g,
bfalse: ff,
can-apply: can-apply(f;x),
do-apply: do-apply(f;x),
isl: isl(x),
outl: outl(x),
all: x:A. B[x],
implies: P 
Q,
prop: 
,
nat: ,
assert: 
b,
le: A 
B,
so_apply: x[s],
so_lambda: x.t[x],
spreadn: spread3,
subtype: S 
T,
has-value: has-value(a),
true: True,
false: False,
not: 
A,
and: P 
Q,
pi2: snd(t),
pi1: fst(t),
squash: 
T,
suptype: suptype(S; T),
cand: A c B,
es-collect-filter: Collect(size v's from X with maximum num[v] such that P[v]),
es-collect-accum: es-collect-accum(X;x.num[x];init;a,v.f[a; v];a.P[a]),
collect_filter: collect_filter(),
uall: [x:A]. B[x],
so_apply: x[s1;s2],
bool: ,
unit: Unit,
iff: P 
Q,
nat_plus: ,
es-E-interface: E(X),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
sq_stable: SqStable(P),
it: 
Lemmas :
bool_wf,
nat_wf,
nat_plus_wf,
eclass_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
in-eclass_wf,
es-interface-top,
iff_weakening_uiff,
assert_wf,
eqtt_to_assert,
not_wf,
uiff_transitivity,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
es-E-interface_wf,
top_wf,
isl_wf,
pi2_wf,
le_wf,
pi1_wf_top,
eq_int_wf,
nat_plus_properties,
assert_of_eq_int,
rational-has-value,
int-rational,
eclass-val_wf,
subtype_base_sq,
bool_subtype_base,
lt_int_wf,
assert_of_lt_int,
le_int_wf,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
btrue_wf,
nat_properties,
int_inc,
ifthenelse_wf,
bfalse_wf,
not_functionality_wrt_uiff,
assert_elim,
list_accum_equality,
false_wf,
sq_stable_from_decidable,
decidable__le,
es-interface-predecessors_wf,
Id_wf,
es-loc_wf,
list_accum_wf,
collectfilteracc2-as_collect_accum,
es-collect-filter_wf,
es-filter-image_wf,
collectfilterfun2_wf,
es-interface-accum_wf,
collect_accum-wf2,
bor_wf,
band_wf,
eclass-ext
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[size:\mBbbN{}\msupplus{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}].
(Collect(size v's from X with maximum num[v] such that P[v])
= collectfilterfun()[es-interface-accum(collectfilteracc(size;v.num[v];v.P[v]);<-1, 0, inr 0 >
X)])
Date html generated:
2011_08_16-PM-05_29_38
Last ObjectModification:
2010_11_10-AM-02_05_22
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