Nuprl Lemma : same-final-iterate-one-one
11,40
postcript
pdf
A
:Type,
f
:(
A
(
A
+ Top)).
SWellFounded(p-graph(
A
;
f
)(
y
,
x
))
p-inject(
A
;
A
;
f
)
(
x
,
y
:
A
.
(final-iterate(
f
;
x
) = final-iterate(
f
;
y
)
A
)
(
n
:
. ((p-graph(
A
;
f
^
n
)(
x
,
y
))
(p-graph(
A
;
f
^
n
)(
y
,
x
)))))
latex
Definitions
x
:
A
.
B
(
x
)
,
Top
,
P
Q
,
p-graph(
A
;
f
)
,
x
:
A
.
B
(
x
)
,
P
Q
,
A
c
B
,
t
T
,
{
T
}
,
,
S
T
,
suptype(
S
;
T
)
,
x
,
y
.
t
(
x
;
y
)
,
True
,
,
T
,
p-inject(
A
;
B
;
f
)
,
P
&
Q
,
A
,
Dec(
P
)
,
A
B
,
False
,
x
(
s1
,
s2
)
Lemmas
final-iterate-property
,
decidable
le
,
can-apply-fun-exp
,
can-apply-fun-exp-add
,
p-fun-exp-injection
,
do-apply
wf
,
p-fun-exp
wf
,
assert
wf
,
can-apply
wf
,
top
wf
,
final-iterate
wf
,
p-inject
wf
,
strongwellfounded
wf
,
p-graph
wf2
,
le
wf
,
squash
wf
,
true
wf
,
bool
wf
,
nat
wf
origin