:: deftheorem Def2 defines LinOrders ARROW:def 2 :
for A being non empty set
for b₂ being Subset of (LinPreorders A) holds
( b₂ = LinOrders A iff for R being Element of LinPreorders A holds
( R in b₂ iff for a, b being Element of A st [a,b] in R & [b,a] in R holds
a = b ) );