theorem
  for f,g being PartFunc of X,Y holds f +* g is PartFunc of X,Y
proof
  let f,g be PartFunc of X,Y;
  rng (f +* g) c= rng f \/ rng g by Th17;
  then
A1: rng(f +* g) c= Y by XBOOLE_1:1;
  dom (f +* g) = dom f \/ dom g by Def1;
  hence thesis by A1,RELSET_1:4;
end;
