let L be non empty antisymmetric upper-bounded RelStr ; :: thesis: for X being non empty Subset of L holds Top L in uparrow X
let X be non empty Subset of L; :: thesis: Top L in uparrow X
A1: uparrow X = { x where x is Element of L : ex y being Element of L st
( x >= y & y in X ) } by WAYBEL_0:15;
consider y being set such that
A2: y in X by XBOOLE_0:def 1;
reconsider y = y as Element of X by A2;
Top L >= y by YELLOW_0:45;
hence Top L in uparrow X by A1; :: thesis: verum