{ 
[Info:Type]. [es:EO+(Info)]. [A:Type]. [X:EClass(A)]. [P:{L:A List|
0 < ||L||}
].
[num:A 
]. [e:E].
Collect(X;x.num[x];L.P[L])(e)
= <num[X(e)], mapfilter(
e.X(e);e'.(num[X(e')] =
num[X(e)]);
(X)(e))>
supposing 
e 
Collect(X;x.num[x];L.P[L]) }
{ Proof }
Definitions occuring in Statement :
es-collect: Collect(X;x.num[x];L.P[L]),
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,
length: ||as||,
eq_int: (i = j),
assert: b,
bool: ,
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s],
and: P 
Q,
less_than: a < b,
set: {x:A| B[x]} ,
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
mapfilter: mapfilter(f;P;L)
Definitions :
so_apply: x[s],
and: P Q,
member: t T,
prop: 
,
top: Top,
so_lambda: 
x.t[x],
all: x:A. B[x],
so_lambda: x y.t[x; y],
cand: A c B,
nat: ,
implies: P 
Q,
le: A B,
subtype: S 
T,
not: 
A,
false: False,
pi2: snd(t),
squash: 
T,
true: True,
uall: [x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
pi1: fst(t),
sq_stable: SqStable(P)
Lemmas :
assert_wf,
in-eclass_wf,
es-collect_wf,
length_wf1,
es-interface-subtype_rel2,
nat_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
top_wf,
bool_wf,
eclass_wf,
eclass-val_wf,
pi1_wf_top,
pi2_wf,
nat_properties,
sq_stable__and,
sq_stable_from_decidable,
decidable__lt,
sq_stable__assert
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:\{L:A List| 0 < ||L||\} {}\mrightarrow{} \mBbbB{}].
\mforall{}[num:A {}\mrightarrow{} \mBbbN{}]. \mforall{}[e:E].
Collect(X;x.num[x];L.P[L])(e)
= <num[X(e)], mapfilter(\mlambda{}e.X(e);\mlambda{}e'.(num[X(e')] =\msubz{} num[X(e)]);\mleq{}(X)(e))>
supposing \muparrow{}e \mmember{}\msubb{} Collect(X;x.num[x];L.P[L])
Date html generated:
2011_08_16-PM-05_26_56
Last ObjectModification:
2010_11_15-AM-01_57_07
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