[:A,A:] c= [:A,A:]
;

then reconsider R =

[:A,A:] as

Relation of

A ;

( ( for a, b being Element of

A holds

(

[a,b] in R or

[b,a] in R ) ) & ( for

a,

b,

c being

Element of

A st

[a,b] in R &

[b,c] in R holds

[a,c] in R ) )

by ZFMISC_1:87;

hence
not LinPreorders A is

empty
by Def1;

verum