Nuprl Lemma : q_trichotomy
11,40
postcript
pdf
r
:rationals. (
qpositive(
r
))
(
r
= 0
rationals)
(
qpositive(-(
r
)))
latex
Definitions
ff
,
tt
,
qinv(
r
)
,
if
b
then
t
else
f
fi
,
qdiv(
r
;
s
)
,
P
Q
,
t
T
,
P
Q
,
prop{i:l}
,
P
Q
,
qeq(
r
;
s
)
,
P
Q
,
r
*
s
,
qpositive(
r
)
,
P
Q
,
x
:
A
.
B
(
x
)
,
decidable(
P
)
,
False
,
A
,
nequal(
T
;
a
;
b
)
,
A
c
B
,
int_nzero
,
x
:
A
.
B
(
x
)
,
subtype(
S
;
T
)
Lemmas
decidable
lt
,
assert
of
eq
int
,
assert
of
lt
int
,
and
functionality
wrt
iff
,
assert
of
band
,
assert
of
bor
,
iff
transitivity
,
eq
int
wf
,
lt
int
wf
,
band
wf
,
bor
wf
,
int
nzero
properties
,
q-elim
,
assert-qeq
,
qeq
wf2
,
qmul
wf
,
int
inc
rationals
,
rationals
wf
,
qpositive
wf
,
assert
wf
,
or
functionality
wrt
iff
origin