reserve X for set;
reserve UN for Universe;

theorem Th102:
  for n being Nat holds sequence_univers.(n+1) = UNIVERSE n
  proof
    let n be Nat;
    sequence_univers.(n+1)
      = GrothendieckUniverse((sequence_univers {}).n) &
    UNIVERSE n
      = (sequence_univers GrothendieckUniverse {}).n by Th46,Th100,Def9;
    hence thesis by Th101;
  end;
