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 Int T c= Fr T
proof
  let x be object;
  assume
A1: x in Fr(Int T);
  then
A2: x in Cl(T`) by XBOOLE_0:def 4;
  Int T = (Cl T`)`;
  then
A3: Cl((Cl T`)`) c= Cl T by Th16,PRE_TOPC:19;
  x in Cl((Cl T`)`) by A1,XBOOLE_0:def 4;
  hence thesis by A2,A3,XBOOLE_0:def 4;
end;
