Nuprl Lemma : pair_support_double_sum
4,23
postcript
pdf
n
,
m
:
,
f
:(
n
m
),
x1
,
x2
:
n
,
y1
,
y2
:
m
.
x1
=
x2
y1
=
y2
(
x
:
n
,
y
:
m
.
(
x
=
x1
&
y
=
y1
)
(
x
=
x2
&
y
=
y2
)
f
(
x
,
y
) = 0)
sum(
f
(
x
,
y
) |
x
<
n
;
y
<
m
) =
f
(
x1
,
y1
)+
f
(
x2
,
y2
)
latex
Definitions
i
j
<
k
,
A
B
,
False
,
P
Q
,
P
&
Q
,
x
(
s1
,
s2
)
,
A
,
Prop
,
{
i
..
j
}
,
t
T
,
,
sum(
f
(
x
;
y
) |
x
<
n
;
y
<
m
)
,
x
:
A
.
B
(
x
)
,
Dec(
P
)
,
P
Q
,
sum(
f
(
x
) |
x
<
k
)
,
x
.
t
(
x
)
,
x
(
s
)
,
SQType(
T
)
,
{
T
}
Lemmas
pair
support
,
empty
support
,
sum
wf
,
singleton
support
sum
,
decidable
int
equal
,
nat
wf
,
int
seg
wf
,
not
wf
origin