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

theorem Th49:
  for X be set holds comp(X,x,y,{}) = {}
proof
  let X be set;
  assume comp(X,x,y,{}) <> {};
  then consider o such that
  A1: o in comp(X,x,y,{}) by XBOOLE_0:def 1;
  consider x1,y1 be Surreal such that
  A2: o = (x1*y) +' (x*y1) +' -' (x1*y1) & x1 in X & y1 in {} by A1,Def14;
  thus thesis by A2;
end;
