Nuprl Lemma : rv-disjoint-rv-partial-sum
11,40
postcript
pdf
p
:FinProbSpace,
f
:(
),
X
:(
n
:
RandomVariable(
p
;
f
(
n
))),
N
:
,
Z
:RandomVariable(
p
;
N
),
n
:
.
(
i
:{0..
n
}.
f
(
i
) <
N
)
(
i
:{0..(
n
- 1)
}. rv-disjoint(
p
;
N
;
X
(
i
);
Z
))
(
k
:{0..
n
}. rv-disjoint(
p
;
N
;rv-partial-sum(
k
;
i
.
X
(
i
));
Z
))
latex
Definitions
x
:
A
.
B
(
x
)
,
,
x
(
s
)
,
P
Q
,
{
i
..
j
}
,
t
T
,
i
j
<
k
,
P
&
Q
,
,
Top
,
S
T
,
i
j
,
A
B
,
A
,
False
,
T
,
True
,
RandomVariable(
p
;
n
)
,
rv-partial-sum(
n
;
i
.
X
(
i
))
,
rv-const(
a
)
,
SQType(
T
)
,
{
T
}
,
suptype(
S
;
T
)
,
x
.
t
(
x
)
,
X
+
Y
,
P
Q
,
P
Q
,
FinProbSpace
,
Dec(
P
)
,
P
Q
Lemmas
random-variable
wf
,
nat
wf
,
finite-prob-space
wf
,
le
wf
,
int
seg
wf
,
rv-disjoint
wf
,
length
wf
nat
,
top
wf
,
rationals
wf
,
nat
properties
,
ge
wf
,
decidable
int
equal
,
rv-disjoint-const
,
int
inc
rationals
,
squash
wf
,
true
wf
,
int-rational
,
sum
unroll
base
q
,
rv-disjoint-rv-add2
,
rv-partial-sum
wf
,
qsum
wf
,
subtype
rel
function
,
qadd
wf
,
sum
unroll
hi
q
origin