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

theorem
  card (L_x) (+) card (R_x) = 0 iff x = 0_No
proof
  hereby assume card (L_x) (+) card (R_x) = 0;
    then L_x={} & R_x={};
    hence x = 0_No;
  end;
  thus thesis;
end;
