reserve X for set,
  Y for non empty set;
reserve n for Nat;

theorem
  n >= 1 implies for P being Subset of Euclid n holds P is bounded
  implies P` is not bounded
proof
  assume
A1: n>=1;
  REAL n c= the carrier of Euclid n;
  then reconsider W = REAL n as Subset of Euclid n;
  let P be Subset of Euclid n;
A2: P \/ P` = [#]Euclid n by PRE_TOPC:2
    .= W;
  assume P is bounded & P` is bounded;
  hence contradiction by A1,A2,JORDAN2C:33,TBSP_1:13;
end;
