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;

theorem
  for p being Point of TOP-REAL 2 ex q being Point of TOP-REAL 2 st q`2
  > N-bound D & p <> q
proof
  let p be Point of TOP-REAL 2;
  take q = |[p`1 - 1,N-bound D + 1]|;
  N-bound D + 1 > N-bound D + 0 by XREAL_1:6;
  hence q`2 > N-bound D;
  thus thesis;
end;
