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

theorem Th35:
  for A being Subset of Niemytzki-plane st A = y=0-line holds Cl A
  = A & Int A = {}
proof
  let A be Subset of Niemytzki-plane;
  assume
A1: A = y=0-line;
  then
A2: A` = y>=0-plane \ y=0-line by Def3;
  thus Cl A = A by A1,Th26,PRE_TOPC:22;
  thus Int A = (Cl A`)` by TOPS_1:def 1
    .= ([#] Niemytzki-plane)` by A2,Th34
    .= {} by XBOOLE_1:37;
end;
