{ 
[Info:Type]. [es:EO+(Info)]. [T,A:Type]. [num:A 
].
[val:A ( 
T?)]. [size:
]. [X:EClass(A)]. [Z:EClass(T)]. [e:E].
Collect(size v's from X
with maximum num= num[v]
return <num,n,outl(v).2> for which
n=outl(val[v]).1 is maximum
or <num,-1,prior Z> if all isr(val[v])))(e)
= <num[X(e)]
, let mx,e' = list-max(e.if isl(val[X(e)])
then fst(outl(val[X(e)]))
else -1
fi ;filter(
e'.(num[X(e')] =
num[X(e)]);
(X)(e)))
in <mx, if (mx = -1) then (Z)'(e) else snd(outl(val[X(e')])) fi >
>
supposing 
e 
Collect(size v's from X
with maximum num= num[v]
return <num,n,outl(v).2> for which
n=outl(val[v]).1 is maximum
or <num,-1,prior Z> if all isr(val[v]))) }
{ Proof }
Definitions occuring in Statement :
es-collect-opt-max: es-collect-opt-max,
es-prior-val: (X)',
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,
outl: outl(x),
isl: isl(x),
eq_int: (i = j),
assert: b,
ifthenelse: if b then t else f fi ,
nat_plus: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
unit: Unit,
lambda: x.A[x],
function: x:A B[x],
spread: spread def,
pair: <a, b>,
product: x:A B[x],
union: left + right,
minus: -n,
natural_number: $n,
int: 
,
universe: Type,
equal: s = t,
filter: filter(P;l),
list-max: list-max(x.f[x];L)
Definitions :
implies: P 
Q,
Id: Id,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
and: P 
Q,
uiff: uiff(P;Q),
axiom: Ax,
pi2: snd(t),
es-prior-val: (X)',
es-interface-predecessors: (X)(e),
eq_int: (i = j),
filter: filter(P;l),
natural_number: $n,
minus: -n,
outl: outl(x),
pi1: fst(t),
isl: isl(x),
list-max: list-max(x.f[x];L),
spread: spread def,
pair: <a, b>,
eclass-val: X(e),
void: Void,
es-E-interface: E(X),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
less_than: a < b,
int: ,
so_apply: x[s],
so_lambda: 
x.t[x],
es-collect-opt-max: es-collect-opt-max,
in-eclass: e X,
prop: 
,
assert: b,
uimplies: b supposing a,
subtype: S 
T,
subtype_rel: A r B,
atom: Atom,
apply: f a,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
ifthenelse: if b then t else f fi ,
record-select: r.x,
event_ordering: EO,
es-E: E,
lambda: x.A[x],
set: {x:A| B[x]} ,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
nat_plus: ,
unit: Unit,
product: x:A B[x],
union: left + right,
nat: ,
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,
inr: inr x ,
real: 
,
grp_car: |g|,
inl: inl x ,
false: False,
length: ||as||,
bool: 
,
es-loc: loc(e),
spreadn: spread4,
map-class: (f[v] where v from X),
btrue: tt,
alle-lt: e<e'.P[e],
sqequal: s ~ t,
es-collect-filter-max: es-collect-filter-max,
es-interface-pair-prior: X;Y,
es-first-at: e is first@ i s.t. e.P[e],
cond-class: [X?Y],
or: P 
Q,
guard: {T},
eq_knd: a = b,
l_member: (x l),
fpf-dom: x dom(f),
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
ExRepD: Error :ExRepD,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
THENM: Error :THENM,
RepUR: Error :RepUR,
MaAuto: Error :MaAuto,
limited-type: LimitedType,
intensional-universe: IType,
sq_type: SQType(T),
bnot: b,
bor: p q,
band: p q,
bimplies: p q,
es-eq-E: e = e',
eq_lnk: a = b,
eq_id: a = b,
eq_str: Error :eq_str,
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-member: deq-member(eq;x;L),
q_le: q_le(r;s),
q_less: q_less(r;s),
qeq: qeq(r;s),
eq_type: eq_type(T;T'),
b-exists: (
i<n.P[i])_b,
bl-exists: (xL.P[x])_b,
bl-all: (xL.P[x])_b,
dcdr-to-bool: [d],
infix_ap: x f y,
grp_blt: a < b,
set_blt: a < b,
null: null(as),
le_int: i z j,
lt_int: i <z j,
eq_bool: p =b q,
iff: P 
Q,
bfalse: ff,
cand: A c B,
mapfilter: mapfilter(f;P;L),
list: type List,
can-apply: can-apply(f;x),
true: True,
exists: x:A. B[x],
select: l[i],
remove-repeats: remove-repeats(eq;L),
last: last(L),
hd: hd(l),
cons: [car / cdr],
map: map(f;as),
rev_implies: P Q,
append: as @ bs,
sq_stable: SqStable(P),
squash: 
T,
fpf-sub: f g,
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
partitions: partitions(I;p),
i-member: r I,
rleq: x y,
rnonneg: rnonneg(r),
req: x = y,
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
nil: [],
tl: tl(l),
Knd: Knd,
locl: locl(a),
IdLnk: IdLnk,
record: record(x.T[x])
Lemmas :
es-E-interface-subtype_rel,
not_functionality_wrt_iff,
squash_wf,
set_subtype_base,
int_subtype_base,
product_subtype_base,
bool_sq,
iff_transitivity,
pi1_wf,
es-interface-val_wf2,
not_functionality_wrt_uiff,
iff_wf,
rev_implies_wf,
map_wf,
list-max-map,
nil_member,
length_wf_nat,
length_wf1,
non_neg_length,
length_cons,
assert_of_eq_int,
es-interface-predecessors-member,
sq_stable__assert,
true_wf,
false_wf,
member_filter,
l_member_wf,
l_member_subtype,
assert_elim,
bool_subtype_base,
subtype_base_sq,
es-loc_wf,
eq_int_wf,
mapfilter_wf,
collect-filter-max-val,
es-prior-val_wf,
is-pair-prior,
bnot_wf,
assert_of_bnot,
eqff_to_assert,
uiff_transitivity,
not_wf,
eqtt_to_assert,
iff_weakening_uiff,
bool_wf,
isl_wf,
intensional-universe_wf,
pair-prior-val,
uiff_inversion,
is-collect-opt-max,
es-collect-filter-max_wf,
es-interface-pair-prior_wf,
map-class-val,
pi1_wf_top,
btrue_wf,
is-map-class,
es-base-E_wf,
es-E_wf,
top_wf,
nat_wf,
subtype_rel_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-collect-opt-max_wf,
es-interface-subtype_rel2,
es-interface-top,
member_wf,
eclass_wf,
in-eclass_wf,
assert_wf,
nat_plus_wf,
unit_wf,
eclass-val_wf,
es-interface-predecessors_wf,
Id_wf,
es-E-interface_wf,
filter_wf,
list-max_wf,
outl_wf,
pi2_wf,
ifthenelse_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T,A:Type]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[val:A {}\mrightarrow{} (\mBbbN{} \mtimes{} T?)]. \mforall{}[size:\mBbbN{}\msupplus{}].
\mforall{}[X:EClass(A)]. \mforall{}[Z:EClass(T)]. \mforall{}[e:E].
Collect(size v's from X
with maximum num= num[v]
return <num,n,outl(v).2> for which
n=outl(val[v]).1 is maximum
or <num,-1,prior Z> if all isr(val[v])))(e)
= <num[X(e)]
, let mx,e' = list-max(e.if isl(val[X(e)]) then fst(outl(val[X(e)])) else -1 fi ;
filter(\mlambda{}e'.(num[X(e')] =\msubz{} num[X(e)]);\mleq{}(X)(e)))
in <mx, if (mx =\msubz{} -1) then (Z)'(e) else snd(outl(val[X(e')])) fi >
>
supposing \muparrow{}e \mmember{}\msubb{} Collect(size v's from X
with maximum num= num[v]
return <num,n,outl(v).2> for which
n=outl(val[v]).1 is maximum
or <num,-1,prior Z> if all isr(val[v])))
Date html generated:
2011_08_16-PM-06_06_42
Last ObjectModification:
2011_06_20-AM-01_48_01
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