
theorem Th2:
  for f being Function, X,Y being set st X c= Y & f|Y is one-to-one
  holds f|X is one-to-one
proof
  let f be Function, X,Y be set such that
A1: X c= Y and
A2: f|Y is one-to-one;
  f|X = (f|Y)|X by A1,RELAT_1:74;
  hence thesis by A2,FUNCT_1:52;
end;
