let L be non empty antisymmetric upper-bounded RelStr ; :: thesis: for X being non empty upper Subset of L holds Top L in X

let X be non empty upper Subset of L; :: thesis: Top L in X

consider y being object such that

A1: y in X by XBOOLE_0:def 1;

reconsider y = y as Element of X by A1;

Top L >= y by YELLOW_0:45;

hence Top L in X by WAYBEL_0:def 20; :: thesis: verum

let X be non empty upper Subset of L; :: thesis: Top L in X

consider y being object such that

A1: y in X by XBOOLE_0:def 1;

reconsider y = y as Element of X by A1;

Top L >= y by YELLOW_0:45;

hence Top L in X by WAYBEL_0:def 20; :: thesis: verum