theorem Th53:
  for f0 being Function of X0,Y st for x being Point of X st x in
  the carrier of X0 holds f.x = f0.x holds f|X0 = f0
proof
  let f0 be Function of X0,Y;
  the carrier of X0 is Subset of X by TSEP_1:1;
  hence thesis by FUNCT_2:96;
end;
