reserve x,y for Real,
  u,v,w for set,
  r for positive Real;

theorem Th34:
  for A being Subset of Niemytzki-plane st A = y>=0-plane \
  y=0-line holds Cl A = [#] Niemytzki-plane
proof
  let A be Subset of Niemytzki-plane;
  A\{A} = A
  proof
    thus A\{A} c= A by XBOOLE_1:36;
    let x be object;
    not A in A;
    hence thesis by ZFMISC_1:56;
  end;
  hence thesis by Th33;
end;
