reserve X for set;
reserve UN for Universe;

theorem
  the empty Grothendieck c< omega c< GrothendieckUniverse {} c<
    GrothendieckUniverse omega
  proof
    set GU0     = GrothendieckUniverse {},
        GUomega = GrothendieckUniverse omega;
    the empty Grothendieck c= omega c= GU0 c= GUomega by Th16,CLASSES3:21;
    hence thesis by Th46,Th43,Th19,Th20,CLASSES3:def 4;
  end;
