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

theorem Th53:
  for X,Y be set holds comp(X,x,y,Y) = comp(Y,y,x,X)
proof
  let X,Y be set;
  comp(X,x,y,Y) c= comp(Y,y,x,X) c= comp(X,x,y,Y) by Lm6;
  hence thesis by XBOOLE_0:def 10;
end;
