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 Th40:
  Int T = T \ Fr T
proof
  (Cl T`)` \/ (Cl T)` = (Cl T /\ Cl T`)` by XBOOLE_1:54;
  then
A1: T \ Fr T = T /\ ((Cl T`)` \/ (Cl T)`) by SUBSET_1:13
    .= (T /\ (Cl T)`) \/ (T /\ Int T) by XBOOLE_1:23;
  T c= Cl T by PRE_TOPC:18;
  then
A2: T misses (Cl T)` by SUBSET_1:24;
  Int T = T /\ Int T by Th16,XBOOLE_1:28;
  then T \ Fr T = {} \/ Int T by A1,A2;
  hence thesis;
end;
