Nuprl Lemma : fpf-sub_wf
11,40
postcript
pdf
A
:Type,
B
:(
A
Type),
eq
:EqDecider(
A
),
f
,
g
:fpf(
A
;
a
.
B
(
a
)).
fpf-sub(
A
;
a
.
B
(
a
);
eq
;
f
;
g
)
prop{i:l}
latex
Definitions
Type
,
t
T
,
x
:
A
B
(
x
)
,
x
:
A
.
B
(
x
)
,
EqDecider(
T
)
,
f
(
a
)
,
x
(
s
)
,
x
.
t
(
x
)
,
fpf(
A
;
a
.
B
(
a
))
,
x
.
A
(
x
)
,
top
,
P
Q
,
fpf-ap(
f
;
eq
;
x
)
,
s
=
t
,
fpf-dom(
eq
;
x
;
f
)
,
b
,
prop{i:l}
,
A
c
B
,
x
:
A
B
(
x
)
,
fpf-sub(
A
;
a
.
B
(
a
);
eq
;
f
;
g
)
Lemmas
assert
wf
,
fpf-dom
wf
,
fpf-ap
wf
,
fpf-trivial-subtype-top
,
fpf
wf
,
deq
wf
origin
A:Type, B:(A
Type), eq:EqDecider(A), f,g:fpf(A; a.B(a)).
prop{i:l} A:Type, B:(AType), eq:EqDecider(A), f,g:fpf(A; a.B(a)).
prop{i:l} TB(x)x:A. B(x)
x. t(x)x.A(x)
Q
b
B
B(x)