Nuprl Lemma : compose-fpf-dom
11,40
postcript
pdf
A
:Type,
B
:(
A
Type),
f
:fpf(
A
;
x
.
B
(
x
)),
C
:Type,
a
:(
A
(?
C
)),
b
:(
C
A
),
y
:
C
.
(
y
fpf-domain(compose-fpf(
a
;
b
;
f
)))
(
x
:
A
. ((
x
fpf-domain(
f
))
((
isl(
a
(
x
))) c
(
y
= outl(
a
(
x
))))))
latex
Definitions
t
T
,
x
(
s
)
,
x
.
t
(
x
)
,
x
:
A
.
B
(
x
)
,
fpf(
A
;
a
.
B
(
a
))
,
Unit
,
b
,
fpf-domain(
f
)
,
compose-fpf(
a
;
b
;
f
)
,
P
Q
,
outl(
x
)
,
isl(
x
)
,
prop{i:l}
,
A
c
B
,
(
x
l
)
,
P
Q
,
x
:
A
.
B
(
x
)
,
P
Q
,
P
Q
,
True
,
T
,
SqStable(
P
)
,
if
b
then
t
else
f
fi
,
,
mapfilter(
f
;
P
;
L
)
Lemmas
iff
functionality
wrt
iff
,
member
map
filter
,
mapfilter
wf
,
sq
stable
from
decidable
,
decidable
assert
,
l
member
wf
,
assert
wf
,
isl
wf
,
outl
wf
,
unit
wf
,
fpf
wf
origin