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;
