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

theorem
 for X,Y be surreal-membered set
    holds X << Y iff --Y << --X
proof
  let X,Y  be surreal-membered set;
  -- -- X = X & -- -- Y = Y by Th15;
  hence thesis by Lm3;
end;
