reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;

theorem Th65:
  A is bounded & B is bounded implies A \/ B is bounded
proof
  assume A is bounded;
  then
A1: A is bounded Subset of Euclid n by JORDAN2C:11;
  then reconsider A as Subset of Euclid n;
  assume B is bounded;
  then
A2: B is bounded Subset of Euclid n by JORDAN2C:11;
  then reconsider B as Subset of Euclid n;
  reconsider E = A \/ B as Subset of Euclid n;
  E is bounded Subset of Euclid n by A1,A2,TBSP_1:13;
  hence thesis by JORDAN2C:11;
end;
