theorem Th15:
  for a being Element of DISJOINT_PAIRS {} holds a = [{},{}]
proof
  let a be Element of DISJOINT_PAIRS {};
  consider x,y being Element of Fin {} such that
A1: a = [x,y] by DOMAIN_1:1;
  x = {} by FINSUB_1:15,TARSKI:def 1;
  hence thesis by A1,FINSUB_1:15,TARSKI:def 1;
end;
