reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem
  for f being Function, X being set st rng f c= X holds (id X)*f = f
proof
  let f be Function, X be set;
  assume rng f c= X;
  then reconsider g = f as Function of dom f, X by FUNCT_2:2;
  (id X)*g = g by FUNCT_2:17;
  hence thesis;
end;
