Nuprl Lemma : proddeq-property
0,22
postcript
pdf
A
,
B
:Type,
a
:EqDecider(
A
),
b
:EqDecider(
B
),
p
,
q
:(
A
B
).
p
=
q
proddeq(
a
;
b
)(
p
,
q
)
latex
Definitions
2of(
t
)
,
1of(
t
)
,
x
.
t
(
x
)
,
proddeq(
a
;
b
)
,
EqDecider(
T
)
,
p
q
,
b
,
Prop
,
t
T
,
P
Q
,
P
Q
,
P
&
Q
,
P
Q
,
x
:
A
.
B
(
x
)
Lemmas
assert
wf
,
band
wf
,
assert
of
band
,
iff
functionality
wrt
iff
,
deq
wf
,
pi1
wf
,
pi2
wf
origin
A, B:Type, a:EqDecider(A), b:EqDecider(B), p, q:(A
B). p = q 
proddeq(a;b)(p,q) A, B:Type, a:EqDecider(A), b:EqDecider(B), p, q:(AB). p = q proddeq(a;b)(p,q) 
x. t(x)
q
b
T
Q Q Qx:A. B(x)