
theorem Lemma:
  for T being set, F being Subset-Family of T holds
    F = { B where B is Subset of T : B in F }
  proof
    let T be set, F be Subset-Family of T;
A1: F c= { B where B is Subset of T : B in F };
    { B where B is Subset of T : B in F } c= F
    proof
      let x be object;
      assume x in { B where B is Subset of T : B in F }; then
      ex B being Subset of T st x = B & B in F;
      hence thesis;
    end;
    hence thesis by A1;
  end;
