theorem
  for D being non empty a_partition of X, W being Element of D
  ex W9 being Element of X st proj(D).W9=W
proof
  let D be non empty a_partition of X, W be Element of D;
  reconsider p = W as Subset of X;
  p <> {} by Def4;
  then consider W9 being Element of X such that
A1: W9 in p by SUBSET_1:4;
  take W9;
  thus thesis by A1,Th65;
end;
