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 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;
