{ 
[Info,A:Type]. [X:EClass(A)]. [P:{L:A List| 0 < ||L||} 
].
[num:A 
].
(Collect(X;x.num[x];L.P[L])
EClass( 
{L:A List| (0 < ||L||) 
(
P[L])} )) }
{ Proof }
Definitions occuring in Statement :
es-collect: Collect(X;x.num[x];L.P[L]),
eclass: EClass(A[eo; e]),
length: ||as||,
assert: b,
bool: ,
nat: ,
uall: [x:A]. B[x],
so_apply: x[s],
and: P Q,
member: t T,
less_than: a < b,
set: {x:A| B[x]} ,
function: x:A B[x],
product: x:A B[x],
list: type List,
natural_number: $n,
universe: Type
Definitions :
bfalse: ff,
guard: {T},
decide_bfalse: decide_bfalse{decide_bfalse_compseq_tag_def:o}(v11.g[v11]; v21.f[v21]),
label: ...$L... t,
null: null(as),
p-outcome: Outcome,
real: 
,
rationals: 
,
proper-iseg: L1 < L2,
iseg: l1 
l2,
add: n + m,
l_exists: (
xL. P[x]),
rev_implies: P 
Q,
iff: P 
Q,
sqequal: s ~ t,
false: False,
multiply: n * m,
gt: i > j,
or: P 
Q,
map: map(f;as),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
l_member: (x l),
void: Void,
cand: A c B,
prop: 
,
bag: bag(T),
pi1: fst(t),
pi2: snd(t),
isl: isl(x),
union: left + right,
implies: P Q,
int: 
,
inr: inr x ,
top: Top,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
collect_filter: collect_filter(),
nil: [],
minus: -n,
pair: <a, b>,
so_lambda: 
x.t[x],
collect_accm: collect_accm(v.P[v];v.num[v]),
es-interface-accum: es-interface-accum(f;x;X),
es-filter-image: f[X],
subtype: S T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
lambda: x.A[x],
all: x:A. B[x],
axiom: Ax,
es-collect: Collect(X;x.num[x];L.P[L]),
apply: f a,
so_apply: x[s],
assert: b,
length: ||as||,
natural_number: $n,
and: P Q,
product: x:A B[x],
equal: s = t,
universe: Type,
so_lambda: x y.t[x; y],
eclass: EClass(A[eo; e]),
bool: ,
set: {x:A| B[x]} ,
less_than: a < b,
list: type List,
uall: [x:A]. B[x],
nat: ,
function: x:A B[x],
isect: 
x:A. B[x],
member: t T,
MaAuto: Error :MaAuto,
Auto: Error :Auto,
CollapseTHENA: Error :CollapseTHENA,
CollapseTHEN: Error :CollapseTHEN
Lemmas :
assert_wf,
length_wf1,
top_wf,
not_wf,
pi2_wf,
isl_wf,
es-filter-image_wf,
le_wf,
nat_wf,
es-interface-accum_wf,
collect_filter-wf2,
collect_accm-wf2,
eclass_wf,
member_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
bool_wf,
pi1_wf_top,
pos_length2,
length_wf_nat,
subtype_rel_wf,
pos-length,
false_wf,
equal-nil-sq-nil,
non_neg_length,
bag_wf,
es-interface-top,
length_nil,
length_wf2,
bfalse_wf
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:\{L:A List| 0 < ||L||\} {}\mrightarrow{} \mBbbB{}]. \mforall{}[num:A {}\mrightarrow{} \mBbbN{}].
(Collect(X;x.num[x];L.P[L]) \mmember{} EClass(\mBbbN{} \mtimes{} \{L:A List| (0 < ||L||) \mwedge{} (\muparrow{}P[L])\} ))
Date html generated:
2011_08_16-PM-05_26_07
Last ObjectModification:
2011_06_20-AM-01_23_43
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