reserve i, j, k, c, m, n for Nat,
  a, x, y, z, X, Y for set,
  D, E for non empty set,
  R for Relation,
  f, g for Function,
  p, q for FinSequence;

theorem
  {} in HFuncs X
proof
  set f = {};
  reconsider f as PartFunc of X*, X by XBOOLE_1:2;
  reconsider f as Element of PFuncs(X*, X) by PARTFUN1:45;
  f in {g where g is Element of PFuncs(X*, X): g is homogeneous};
  hence thesis;
end;
