reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem Th30:
  for D being non empty a_partition of the carrier of X holds rng
  Proj D = the carrier of space D
proof
  let D be non empty a_partition of the carrier of X;
  thus rng Proj D c= the carrier of space D;
  let e be object;
  assume e in the carrier of space D;
  then ex p being Point of X st (Proj D).p = e by Th29;
  hence thesis by FUNCT_2:4;
end;
