RelStr(# a, the well-ordering upper-bounded Order of a #) is object of (W -INF_category) by A1, Def4;
then reconsider b = RelStr(# a, the well-ordering upper-bounded Order of a #) as object of (W -INF(SC)_category) by Def10;
b = latt b ;
then A2: ex b being object of (W -INF(SC)_category) st S₁[b] ;
thus ex B being non empty strict full subcategory of W -INF(SC)_category st
for a being object of (W -INF(SC)_category) holds
( a is object of B iff S₁[a] ) from YELLOW20:sch 2(A2); :: thesis: verum