reserve A,B,C for Ordinal,
        o for object,
        x,y,z,t,r,l for Surreal,
        X,Y for set;

theorem Th27:
  for X be set holds X++{} = {}
proof
  let X be set;
  assume X++{} <> {};
  then consider x be object such that
  A1:x in X++{} by XBOOLE_0:def 1;
  ex a,b be Surreal st a in X & b in {}& x=a+b by Def8,A1;
  hence thesis;
end;
