reserve TS for 1-sorted,
  K, Q for Subset of TS;
reserve TS for TopSpace,
  GX for TopStruct,
  x for set,
  P, Q for Subset of TS,
  K , L for Subset of TS,
  R, S for Subset of GX,
  T, W for Subset of GX;

theorem Th6:
  Cl K \ Cl L c= Cl(K \ L)
proof
  let x be object;
  Cl K \/ Cl L = Cl (K \/ L) by PRE_TOPC:20
    .= Cl((K \ L) \/ L) by XBOOLE_1:39
    .= Cl(K \ L) \/ Cl L by PRE_TOPC:20;
  then
A1: x in Cl K \/ Cl L iff x in Cl(K \ L) or x in Cl L by XBOOLE_0:def 3;
  assume
A2: x in (Cl K \ Cl L);
  then x in Cl K by XBOOLE_0:def 5;
  hence thesis by A2,A1,XBOOLE_0:def 3,def 5;
end;
