theorem Th28:
  for P, A, a st a in Polish-expression-set(P, A)
      ex n st a in Polish-expression-hierarchy(P, A, n+1)
proof
  let P, A, a;
  assume A1: a in Polish-expression-set(P, A);
  set Y = the set of all Polish-expression-hierarchy(P, A, n) where
    n is Nat;
  consider X such that A2: a in X and A3: X in Y by A1, TARSKI:def 4;
  consider n such that A4: X = Polish-expression-hierarchy(P, A, n) by A3;
  Polish-expression-hierarchy(P, A, n)
      c= Polish-expression-hierarchy(P, A, n+1) by Th24;
  hence thesis by A2, A4;
end;
