theorem
  "\/"{a} = a & "/\"{a} = a
proof
A1: a in {a} by TARSKI:def 1;
  {a} is_less_than a
  proof
    let b;
    assume b in {a};
    hence b [= a by TARSKI:def 1;
  end;
  hence "\/"{a} = a by A1,Th40;
  a is_less_than {a}
  proof
    let b;
    assume b in {a};
    hence a [= b by TARSKI:def 1;
  end;
  hence thesis by A1,Th41;
end;
