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

theorem Th35:
  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,W9 being Point of XX
st not W in the carrier of X & Proj(TrivExt D).W=Proj(TrivExt D).W9 holds W=W9
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,W9 be Point of XX;
  assume not W in the carrier of X;
  then
A1: Proj TrivExt D.W = {W} by Th34;
  W9 in Proj TrivExt D.W9 by EQREL_1:def 9;
  hence thesis by A1,TARSKI:def 1;
end;
