 reserve Exx for Real;

theorem
  ex A being SetSequence of NAT st for n being Nat holds A.n = {n}
proof
  deffunc U(Nat) = {In($1,NAT)};
AA: for x being Element of NAT holds U(x) in bool NAT
  proof
    let x be Element of NAT;
    U(x) c= NAT by ZFMISC_1:31;
    hence thesis;
  end;
  consider f being SetSequence of NAT such that
A1: for d be Element of NAT holds f.d = U(d) from FUNCT_2:sch 8(AA);
  take f;
  let n be Nat;
  reconsider n as Element of NAT by ORDINAL1:def 12;
  f.n = U(n) by A1;
  hence thesis;
end;
