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
  P is condensed implies Int Fr P = {}
proof
  set x = the Element of Int(Fr P);
  assume
A1: P is condensed;
  then P c= Cl(Int P);
  then
A2: (Cl(Int P))` c= P` by SUBSET_1:12;
  assume
A3: Int(Fr P) <> {};
  then reconsider x99= x as Point of TS by TARSKI:def 3;
A4: Int(Fr P) = (Cl(((Cl P)`) \/ (Cl P`)`))` by XBOOLE_1:54
    .= (Cl(((Cl P)`)) \/ Cl((Cl P`))`)` by PRE_TOPC:20
    .= Int(Cl P) /\ (Cl(Int P))` by XBOOLE_1:53;
  then
A5: x99 in Int(Cl P) by A3,XBOOLE_0:def 4;
A6: x99 in (Cl(Int P))` by A4,A3,XBOOLE_0:def 4;
  Int(Cl P) c= P by A1;
  hence contradiction by A2,A5,A6,XBOOLE_0:def 5;
end;
