{ 
[Info,T,A:Type]. [num:A 
]. [val:A ( 
T?)]. [size:
].
[X:EClass(A)]. [Z:EClass(T)].
(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]))) 
EClass( 
T)) }
{ Proof }
Definitions occuring in Statement :
es-collect-opt-max: es-collect-opt-max,
eclass: EClass(A[eo; e]),
nat_plus: ,
nat: ,
uall: [x:A]. B[x],
so_apply: x[s],
unit: Unit,
member: t T,
function: x:A B[x],
product: x:A B[x],
union: left + right,
int: ,
universe: Type
Definitions :
uall: [x:A]. B[x],
member: t T,
es-collect-opt-max: es-collect-opt-max,
so_apply: x[s],
spreadn: spread4,
ifthenelse: if b then t else f fi ,
btrue: tt,
top: Top,
all: x:A. B[x],
subtype: S 
T,
so_lambda: 
x.t[x],
implies: P 
Q,
prop: 
,
bfalse: ff,
so_lambda: x y.t[x; y],
nat: ,
unit: Unit,
bool: 
,
iff: P 
Q,
and: P 
Q,
uimplies: b supposing a,
so_apply: x[s1;s2],
it: 
Lemmas :
map-class_wf,
nat_wf,
pi1_wf_top,
isl_wf,
unit_wf,
bool_wf,
iff_weakening_uiff,
assert_wf,
eqtt_to_assert,
pi2_wf,
outl_wf,
not_wf,
uiff_transitivity,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
es-interface-pair-prior_wf,
es-collect-filter-max_wf,
btrue_wf,
eclass_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
nat_plus_wf
\mforall{}[Info,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)].
(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]))) \mmember{} EClass(\mBbbN{} \mtimes{} \mBbbZ{} \mtimes{} T))
Date html generated:
2011_08_16-PM-05_39_43
Last ObjectModification:
2011_06_20-AM-01_29_40
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