reserve X for set;
reserve UN for Universe;

theorem Th98:
  for n being Nat holds Tarski-Class ((sequence_univers FinSETS).n)
    = GrothendieckUniverse ((sequence_univers FinSETS).n)
  proof
    let n be Nat;
    per cases;
    suppose n = 0;
      then Tarski-Class ((sequence_univers FinSETS).n) = SETS &
        GrothendieckUniverse ((sequence_univers FinSETS).n) = SETS
        by Th77,Def9;
      hence thesis;
    end;
    suppose n <> 0;
      then consider m be Nat such that
A1:   n = m + 1 by NAT_1:6;
      (sequence_univers FinSETS).n
        = GrothendieckUniverse ((sequence_univers FinSETS).m) by A1,Def9;
      hence thesis by CLASSES3:22;
    end;
  end;
