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

theorem
  x <= y & z = [{x,y},X] & t = [{y},X] implies z==t
proof
  assume A1:x <= y & z = [{x,y},X] & t = [{y},X];
  A2: for s be Surreal st s in L_z holds s <= y
     by A1,TARSKI:def 2;
  A3:y in L_z by A1,TARSKI:def 2;
  t = [{y},R_z] by A1;
  hence thesis by A2,A3,Th23;
end;
