Nuprl Lemma : es-collect-filter-max_wf
[Info,A:Type]. [f:A 
]. [X:EClass(A)]. [size:
]. [num:A ]. [P:A 
].
(Collect(size v's from X with maximum num[v] such that P[v] return <num[v],n,v> with n = maximum f[v])
EClass( 
i: {v:A| f[v] = i} ))
Proof not projected
Definitions occuring in Statement :
es-collect-filter-max: Collect(size v's from X with maximum num[v] such that P[v] return <num[v],n,v> with n = maximum f[v]),
eclass: EClass(A[eo; e]),
bool: ,
nat_plus: ,
nat: ,
uall: [x:A]. B[x],
so_apply: x[s],
member: t T,
set: {x:A| B[x]} ,
function: x:A B[x],
product: x:A B[x],
int: ,
universe: Type,
equal: s = t
Definitions :
so_lambda: 
x y.t[x; y],
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: x.t[x],
assert: 
b,
pi2: snd(t),
pi1: fst(t),
es-collect-filter-max: Collect(size v's from X with maximum num[v] such that P[v] return <num[v],n,v> with n = maximum f[v]),
so_apply: x[s],
member: t T,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
guard: {T},
implies: P 
Q,
all: x:A. B[x],
sq_type: SQType(T),
uimplies: b supposing a,
prop: 
,
subtype: S 
T
Lemmas :
assert_elim,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
eclass_wf,
nat_plus_wf,
es-collect-filter-max-aux_wf,
bool_subtype_base,
bool_wf,
subtype_base_sq,
outl_wf,
isl_wf,
assert_wf,
top_wf,
nat_wf,
map-class_wf
\mforall{}[Info,A:Type]. \mforall{}[f:A {}\mrightarrow{} \mBbbZ{}]. \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]
return <num[v],n,v> with n = maximum f[v]) \mmember{} EClass(\mBbbN{} \mtimes{} i:\mBbbZ{} \mtimes{} \{v:A| f[v] = i\} ))
Date html generated:
2012_01_23-PM-12_27_51
Last ObjectModification:
2011_12_13-PM-02_04_56
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