reserve X for set;
reserve UN for Universe;

theorem Th99:
  for n being Nat holds UNIVERSE n in UNIVERSE (n+1)
  proof
    let n be Nat;
    succ Segm n = Segm(n + 1) by NAT_1:38;
    then UNIVERSE (n+1) = Tarski-Class (UNIVERSE n) by CLASSES2:66
                       .= GrothendieckUniverse (UNIVERSE n) by CLASSES3:22;
    hence thesis by CLASSES3:def 4;
  end;
