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

theorem
  x==y implies [L_x\/L_y,R_x\/R_y] is Surreal
proof
  assume A1: x==y;
  L_x << {x} << R_x by Th11;
  then L_x << {y} << R_x by A1,Th17,Th18;
  hence thesis by Th14;
end;
