theorem Th16:
  DISJOINT_PAIRS {} = {[{},{}]}
proof
  thus DISJOINT_PAIRS {} c= {[{},{}]}
  proof
    let x be object;
    assume x in DISJOINT_PAIRS {};
    then x = [{},{}] by Th15;
    hence thesis by TARSKI:def 1;
  end;
  thus {[{},{}]} c= DISJOINT_PAIRS {}
  proof
    let x be object;
    assume x in {[{},{}]};
    then x = [{},{}] by TARSKI:def 1;
    then x is Element of DISJOINT_PAIRS {} by Th12;
    hence thesis;
  end;
end;
