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;
