Nuprl Lemma : symmetrized_preorder
13,42
postcript
pdf
T
:Type,
R
:(
T
T
). Preorder(
T
;
x
,
y
.
R
(
x
,
y
))
EquivRel(
T
;
a
,
b
.Symmetrize(
x
,
y
.
R
(
x
,
y
);
a
;
b
))
latex
Up
rel
1
,
rel
1
Definitions
x
,
y
.
t
(
x
;
y
)
,
t
T
,
P
&
Q
,
Symmetrize(
x
,
y
.
R
(
x
;
y
);
a
;
b
)
,
EquivRel(
T
;
x
,
y
.
E
(
x
;
y
))
,
x
(
s1
,
s2
)
,
Preorder(
T
;
x
,
y
.
R
(
x
;
y
))
,
P
Q
,
,
x
:
A
.
B
(
x
)
,
Refl(
T
;
x
,
y
.
E
(
x
;
y
))
,
Sym(
T
;
x
,
y
.
E
(
x
;
y
))
,
Trans(
T
;
x
,
y
.
E
(
x
;
y
))
Lemmas
trans
wf
,
refl
wf
origin
T:Type, R:(T
T
). Preorder(T;x,y.R(x,y)) 
EquivRel(T;a,b.Symmetrize(x,y.R(x,y);a;b)) T:Type, R:(TT). Preorder(T;x,y.R(x,y)) EquivRel(T;a,b.Symmetrize(x,y.R(x,y);a;b)) 
x,y. t(x;y)
T Qx:A. B(x)