
theorem Th14:
  for X,Y being non empty set, P being a_partition of Y
  for f being Function of X, P st P c= rng f & f is one-to-one
  holds f is IndexedPartition of Y
proof
  let X,Y be non empty set, P be a_partition of Y;
  let f be Function of X, P;
  assume P c= rng f;
  then rng f = P;
  hence thesis by Def2;
end;
