reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

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;
