Nuprl Lemma : prod-deq_wf
0,22
postcript
pdf
A
,
B
:Type,
a
:EqDecider(
A
),
b
:EqDecider(
B
).
prod-deq(
A
;
B
;
a
;
b
)
(
p
,
q
:(
A
B
).
p
=
q
proddeq(
a
;
b
)(
p
,
q
))
latex
Definitions
proddeq-property
,
p
q
,
b
,
assert
of
band
,
iff
functionality
wrt
iff
,
prod-deq-aux{v:l,i:l}(
A
;
B
;
a
;
b
)
,
prod-deq(
A
;
B
;
a
;
b
)
,
P
Q
,
P
&
Q
,
P
Q
,
EqDecider(
T
)
,
x
:
A
.
B
(
x
)
,
t
T
Lemmas
prod-deq-aux
wf
,
deq
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)) 
q
b Q
Qx:A. B(x) T