reserve A for non empty set,
  a for Element of A;
reserve A for set;
reserve B,C for Element of Fin DISJOINT_PAIRS A,
  x for Element of [:Fin A, Fin A:],
  a,b,c,d,s,t,s9,t9,t1,t2,s1,s2 for Element of DISJOINT_PAIRS A,
  u,v,w for Element of NormForm A;
reserve K,L for Element of Normal_forms_on A;
reserve f,f9 for (Element of Funcs(DISJOINT_PAIRS A, [:Fin A,Fin A:])),
  g,h for Element of Funcs(DISJOINT_PAIRS A, [A]);

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;
