reserve X,Y,Z for set,
        x,y,z for object,
        A,B,C for Ordinal;
reserve U for Grothendieck;

theorem
  for X be infinite set holds
    Tarski-Class {X} c< GrothendieckUniverse {X}
proof
  let X be infinite set;
  thus Tarski-Class {X} c= GrothendieckUniverse {X} by Th18;
  GrothendieckUniverse {X} is union-closed;
  then union {X} in GrothendieckUniverse {X} by Def4;
  hence thesis by Th19;
end;
