reserve FT for non empty RelStr;
reserve A for Subset of FT;
reserve T for non empty TopStruct;
reserve FMT for non empty FMT_Space_Str;
reserve x, y for Element of FMT;
reserve A, B, W, V for Subset of FMT;

theorem
  A^Fodelta = (A^Fodel_i) \/ (A^Fodel_o)
proof
  for x being object
    holds x in (A^Fodelta) iff x in (A^Fodel_i) \/ (A ^Fodel_o )
  proof
    let x be object;
    thus x in A^Fodelta implies x in (A^Fodel_i) \/ (A^Fodel_o)
    proof
      assume x in A^Fodelta;
      then x in [#](the carrier of FMT) /\ (A^Fodelta) by XBOOLE_1:28;
      then x in (A \/ A`) /\ (A^Fodelta) by SUBSET_1:10;
      hence thesis by XBOOLE_1:23;
    end;
    assume x in (A^Fodel_i) \/ (A^Fodel_o);
    then x in (A \/ A`) /\ (A^Fodelta) by XBOOLE_1:23;
    then x in [#](the carrier of FMT) /\ (A^Fodelta) by SUBSET_1:10;
    hence thesis by XBOOLE_1:28;
  end;
  hence thesis by TARSKI:2;
end;
