reserve X for TopStruct,
  A for Subset of X;
reserve X for TopSpace,
  A,B for Subset of X;

theorem Th7:
  A misses Int Cl A implies Int Cl A = {}
proof
  reconsider A9 = A as Subset of X;
  assume A /\ Int Cl A = {};
  then A9 misses Int Cl A9;
  then (Cl A) misses (Int Cl A) by TSEP_1:36;
  then (Cl A) /\ (Int Cl A) = {};
  hence thesis by TOPS_1:16,XBOOLE_1:28;
end;
