reserve a, r, s for Real;

theorem Th4:
  for T being TopSpace, S being SubSpace of T, A being Subset of T,
  B being Subset of S st A = B holds T|A = S|B
proof
  let T be TopSpace, S be SubSpace of T, A be Subset of T, B be Subset of S;
  assume A = B;
  then S|B is SubSpace of T & [#](S|B) = A by PRE_TOPC:def 5,TSEP_1:7;
  hence thesis by PRE_TOPC:def 5;
end;
