RelStr(# a,r #) is object of by A1, Def5;
then reconsider b = RelStr(# a,r #) as object of by Def11;
b = latt b ;
then A2: ex b being object of st S₁[b] ;
thus ex B being non empty strict full subcategory of non empty strict full st
for a being object of holds
( a is object of iff S₁[a] ) from YELLOW20:sch 2(A2); :: thesis: verum