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

theorem Th36:
  (y>=0-plane \ y=0-line) /\ product <*RAT,RAT*> is dense Subset
  of Niemytzki-plane
proof
  (y>=0-plane \ y=0-line) /\ product <*RAT,RAT*> c= y>=0-plane \ y=0-line
  by XBOOLE_1:17;
  then reconsider
  A = (y>=0-plane \ y=0-line) /\ product <*RAT,RAT*> as Subset of
  Niemytzki-plane by Th25,XBOOLE_1:1;
  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;
  then Cl A = [#] Niemytzki-plane by Th32;
  hence thesis by TOPS_1:def 3;
end;
