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

theorem
  y=0-line is nowhere_dense Subset of Niemytzki-plane
proof
  reconsider A = y=0-line as Subset of Niemytzki-plane by Def3,Th19;
  Int Cl A = Int A by Th26,PRE_TOPC:22
    .= {} by Th35;
  hence thesis by TOPS_3:def 3;
end;
