{ 
[A:Type]
d:A List. f1:a:{a:A| (a 
d)} 
Top. x:A. eq:EqDecider(A).
((x d)
(
i:
||d||
((j:i. (
((fst(map(
x.<x, f1 x>;d)[j])) = x)))
((fst(map(x.<x, f1 x>;d)[i])) = x)))) }
{ Proof }
Definitions occuring in Statement :
select: l[i],
map: map(f;as),
length: ||as||,
int_seg: {i..j
},
uall: [x:A]. B[x],
top: Top,
pi1: fst(t),
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
l_member: (x l),
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
exists: x:A. B[x],
member: t T,
and: P Q,
top: Top,
int_seg: {i..j},
pi1: fst(t),
subtype: S 
T,
lelt: i 
j < k,
not: A,
prop: 
,
le: A B,
false: False,
uimplies: b supposing a
Lemmas :
l_member-first,
l_member_wf,
deq_wf,
top_wf,
int_seg_wf,
select-map,
length_wf1,
le_wf,
not_wf,
select_wf
\mforall{}[A:Type]
\mforall{}d:A List. \mforall{}f1:a:\{a:A| (a \mmember{} d)\} {}\mrightarrow{} Top. \mforall{}x:A. \mforall{}eq:EqDecider(A).
((x \mmember{} d)
{}\mRightarrow{} (\mexists{}i:\mBbbN{}||d||
((\mforall{}j:\mBbbN{}i. (\mneg{}((fst(map(\mlambda{}x.<x, f1 x>d)[j])) = x))) \mwedge{} ((fst(map(\mlambda{}x.<x, f1 x>d)[i])) = x))))
Date html generated:
2011_08_10-AM-07_55_50
Last ObjectModification:
2011_06_18-AM-08_16_53
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