reserve T for TopSpace;

theorem Th1:
  for A being Subset of T holds Int Cl Int A c= Int Cl A & Int Cl
  Int A c= Cl Int A
proof
  let A be Subset of T;
  Cl Int A c= Cl A by PRE_TOPC:19,TOPS_1:16;
  hence Int Cl Int A c= Int Cl A by TOPS_1:19;
  thus thesis by TOPS_1:16;
end;
