
theorem
  for T being non empty TopSpace, A being Subset of T holds Der A = { x
  where x is Point of T : x in Cl (A \ {x}) }
proof
  let T be non empty TopSpace, A be Subset of T;
  thus Der A c= { x where x is Point of T : x in Cl (A \ {x}) }
  proof
    let x be object;
    assume x in Der A;
    then x is_an_accumulation_point_of A by TOPGEN_1:def 3;
    then x in Cl (A \ {x}) by TOPGEN_1:def 2;
    hence thesis;
  end;
  let y be object;
  assume y in { x where x is Point of T : x in Cl (A \ {x}) };
  then consider z being Point of T such that
A1: z = y and
A2: z in Cl (A \ {z});
  z is_an_accumulation_point_of A by A2,TOPGEN_1:def 2;
  hence thesis by A1,TOPGEN_1:def 3;
end;
