
theorem Th5:
  for f,g being Function, x,X being set holds
  x nin X & x in dom g implies ((f,X)+*g).x = g.x
proof
  let f,g be Function;
  let x,X be set;
  assume x nin X;
  then x nin dom f /\ X by XBOOLE_0:def 4;
  then x nin dom (f|X) by RELAT_1:61;
  hence thesis by FUNCT_4:11;
end;
