:: deftheorem Def1 defines LinPreorders ARROW:def 1 :
for A being non empty set
for b₂ being set holds
( b₂ = LinPreorders A iff for R being set holds
( R in b₂ iff ( R is 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 ) ) ) );