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,{x,y}] & t = [X,{x}] implies z==t
proof
  assume A1:x <= y & z = [X,{x,y}] & t = [X,{x}];
  A2: for s be Surreal st s in R_z holds x <= s
    by A1,TARSKI:def 2;
  A3:  x in R_z by A1,TARSKI:def 2;
  t = [L_z,{x}] by A1;
  hence thesis by A2,A3,Th24;
end;
