reserve X for TopSpace;

theorem
  for X being strict TopStruct holds X|[#]X = X
proof
  let X be strict TopStruct;
  reconsider X0 = X as SubSpace of X by Th2;
  reconsider P = [#]X0 as Subset of X;
  X|P = X0 by PRE_TOPC:def 5;
  hence thesis;
end;
