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

theorem
  y>=0-plane \ y=0-line is dense Subset of Niemytzki-plane
proof
  reconsider A = y>=0-plane \ y=0-line as open Subset of Niemytzki-plane by
Th25;
  Cl A = [#] Niemytzki-plane by Th34;
  hence thesis by TOPS_1:def 3;
end;
