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

theorem Th33:
  for XX being non empty TopSpace, X being non empty SubSpace of
XX, D being non empty a_partition of the carrier of X, W being Point of XX st W
  in the carrier of X holds Proj(TrivExt D).W=Proj(D).W
proof
  let XX be non empty TopSpace, X be non empty SubSpace of XX, D be non empty
  a_partition of the carrier of X, W be Point of XX;
  assume
A1: W in the carrier of X;
  then reconsider p = W as Point of X;
  D c= TrivExt D & proj D.p in D by XBOOLE_1:7;
  then reconsider A = Proj D.W as Element of TrivExt D;
  W in A by A1,EQREL_1:def 9;
  hence thesis by EQREL_1:65;
end;
