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

theorem Th29:
  for D being non empty a_partition of the carrier of X, W being
  Point of space D ex W9 being Point of X st Proj(D).W9=W
proof
  let D be non empty a_partition of the carrier of X, W be Point of space D;
  reconsider p = W as Element of D by Def7;
  consider W9 being Point of X such that
A1: (proj D).W9 = p by EQREL_1:68;
  take W9;
  thus thesis by A1;
end;
