Nuprl Lemma : swap_cons
4,23
postcript
pdf
T
:Type,
L
:
T
List,
x
:
T
,
i
,
j
:{1..(||
L
||+1)
}. swap(
x
.
L
;
i
;
j
) = (
x
.swap(
L
;
i
-1;
j
-1))
latex
Definitions
,
t
T
,
x
:
A
.
B
(
x
)
,
swap(
L
;
i
;
j
)
,
||
as
||
,
Prop
,
i
j
,
{
i
..
j
}
,
P
Q
,
False
,
A
,
P
&
Q
,
A
B
,
i
j
<
k
,
P
Q
,
P
Q
,
{
T
}
,
SQType(
T
)
,
P
Q
,
Dec(
P
)
,
hd(
l
)
,
i
<
j
,
i
j
,
l
[
i
]
,
b
,
b
,
,
Unit
,
if
b
t
else
f
fi
,
i
=
j
,
(
i
,
j
)
,
True
,
T
Lemmas
squash
wf
,
true
wf
,
select
cons
tl
,
select
wf
,
bool
wf
,
ifthenelse
wf
,
eq
int
wf
,
eqtt
to
assert
,
eqff
to
assert
,
iff
transitivity
,
assert
of
bnot
,
not
functionality
wrt
iff
,
assert
of
eq
int
,
bnot
wf
,
not
wf
,
assert
wf
,
swap
select
,
le
wf
,
decidable
int
equal
,
add
functionality
wrt
eq
,
swap
length
,
int
seg
wf
,
list
extensionality
,
length
cons
,
non
neg
length
,
swap
wf
,
length
wf1
,
nat
wf
origin