:: deftheorem defines has_lower_Zorn_property_wrt ORDERS_1:def 11 :
for R being Relation
for X being set holds
( X has_lower_Zorn_property_wrt R iff for Y being set st Y c= X & R |_2 Y is being_linear-order holds
ex x being set st
( x in X & ( for y being set st y in Y holds
[x,y] in R ) ) );