reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;
reserve A,B for non empty set;
reserve Y for non empty set,
  f for Function of X,Y,
  p for PartFunc of Y,Z,
  x for Element of X;
reserve g for Function of X,X;
reserve X,Y for non empty set,
  Z,S,T for set,
  f for Function of X,Y,
  g for PartFunc of Y,Z,
  x for Element of X;

theorem
  for X being set, Y being non empty set
  for f being Function of X, Y, g being X-valued Function
   holds dom(f*g) = dom g
proof
  let X be set, Y be non empty set;
  let f be Function of X, Y;
  let g be X-valued Function;
  dom f = X by Def1;
  then rng g c= dom f;
  hence thesis by RELAT_1:27;
end;
