theorem LemS:
  dom (a<->b) = {a,b} & (a<->b).a = b & (a<->b).b = a & rng (a<->b) = {a,b}
  proof
    [a,b] in a<->b & [b,a] in a<->b by TARSKI:def 2;
    hence thesis by RELAT_1:10,FUNCT_1:1;
  end;
