Nuprl Lemma : order_functionality_wrt_iff
13,42
postcript
pdf
T
:Type,
R
,
R'
:(
T
T
).
(
x
,
y
:
T
.
R
(
x
,
y
)
R'
(
x
,
y
))
(Order(
T
;
x
,
y
.
R
(
x
,
y
))
Order(
T
;
x
,
y
.
R'
(
x
,
y
)))
latex
Up
rel
1
,
rel
1
Definitions
P
Q
,
P
&
Q
,
t
T
,
Order(
T
;
x
,
y
.
R
(
x
;
y
))
,
x
(
s1
,
s2
)
,
P
Q
,
P
Q
,
,
x
:
A
.
B
(
x
)
,
x
,
y
.
t
(
x
;
y
)
Lemmas
iff
wf
,
anti
sym
functionality
wrt
iff
,
trans
functionality
wrt
iff
,
refl
functionality
wrt
iff
,
and
functionality
wrt
iff
,
iff
functionality
wrt
iff
,
anti
sym
wf
,
trans
wf
,
refl
wf
,
order
wf
origin
T:Type, R, R':(T
T
).
x, y:T. R(x,y) 
R'(x,y)) (Order(T;x,y.R(x,y)) Order(T;x,y.R'(x,y))) T:Type, R, R':(TT).
x, y:T. R(x,y) R'(x,y)) (Order(T;x,y.R(x,y)) Order(T;x,y.R'(x,y))) 
T
x,y. t(x;y)