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 Th34:
  Fr Fr T c= Fr T
proof
  let x be object;
  assume x in Fr(Fr T);
  then
A1: x in Cl(Cl T /\ Cl(T`)) by XBOOLE_0:def 4;
  Cl(Cl T /\ Cl(T`)) c= Cl(Cl T) /\ Cl(Cl(T`)) by PRE_TOPC:21;
  hence thesis by A1;
end;
