reserve T for TopSpace;

theorem Th2:
  for A being Subset of T holds Cl Int A c= Cl Int Cl A & Int Cl A
  c= Cl Int Cl A
proof
  let A be Subset of T;
  Int A c= Int Cl A by PRE_TOPC:18,TOPS_1:19;
  hence Cl Int A c= Cl Int Cl A by PRE_TOPC:19;
  thus thesis by PRE_TOPC:18;
end;
