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
  Fr Fr Fr K = Fr Fr K
proof
A1: Int Fr Fr K = {} by Lm4;
  Fr Fr Fr K = Cl(Fr(Fr K)) \ Int(Fr(Fr K)) by Lm2
    .= Fr Fr K by A1,Lm3;
  hence thesis;
end;
