Nuprl Lemma : weak-antecedent-conditional
11,40
postcript
pdf
es
:ES,
P1
,
Q1
,
P2
,
Q2
:(E
),
dcd_P1
:(
e
:E
Dec(
P1
(
e
))),
f
:({
e
:E|
P1
(
e
)}
{
e
:E|
Q1
(
e
)} ),
g
:({
e
:E|
P2
(
e
)}
{
e
:E|
Q2
(
e
)} ).
(
Q1
==
f
==
P1
&
Q2
==
g
==
P2
)
e
.(
Q1
(
e
))
(
Q2
(
e
))
==[
P1
?
f
:
g
]==
e
.(
P1
(
e
))
(
P2
(
e
))
latex
Definitions
f
(
a
)
,
left
+
right
,
Q
==
f
==
P
,
P
Q
,
P
&
Q
,
x
:
A
B
(
x
)
,
P
Q
,
E
,
{
x
:
A
|
B
(
x
)}
,
x
:
A
B
(
x
)
,
x
:
A
.
B
(
x
)
,
Dec(
P
)
,
Type
,
,
ES
,
t
T
,
e
c
e'
,
s
=
t
,
if
p
:
P
then
A
(
p
) else
B
fi
,
[
P
?
f
:
g
]
,
False
,
A
,
(
e
<
e'
)
,
S
T
,
suptype(
S
;
T
)
,
{
T
}
,
b
,
t
.1
Lemmas
conditional
wf
,
es-E
wf
origin