reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem
  for TS being TopStruct, A, B being Subset of TS st A <> B holds A` <> B`
proof
  let TS be TopStruct, A, B be Subset of TS;
  assume
A1: A <> B;
  assume A` = B`;
  then A = B``;
  hence thesis by A1;
end;
