reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem Th14:
  for X, Y being TopSpace, A being Subset of [:X,Y:] holds Int A =
  union Base-Appr A
proof
  let X, Y be TopSpace, A be Subset of [:X,Y:];
  Int A = union Base-Appr Int A & Base-Appr Int A c= Base-Appr A by Th11,Th13,
TOPS_1:16;
  hence Int A c= union Base-Appr A by ZFMISC_1:77;
  union Base-Appr A is open by TOPS_2:19;
  hence thesis by Th12,TOPS_1:24;
end;
