reserve k,m,n for Nat,
  a, b, c for object,
  x, y, X, Y, Z for set,
  D for non empty set;
reserve p, q, r, s, t, u, v for FinSequence;
reserve P, Q, R, P1, P2, Q1, Q2, R1, R2 for FinSequence-membered set;
reserve S, T for non empty FinSequence-membered set;
reserve A for Function of P, NAT;
reserve U, V, W for Subset of P*;

theorem Th26:
  for P, A, n holds Polish-expression-hierarchy(P, A, n)
      c= Polish-expression-set(P, A)
proof
  let P, A, n;
  set Q = Polish-expression-hierarchy(P, A, n);
  set X = the set of all Polish-expression-hierarchy(P, A, m) where m is Nat;
  let a;
  assume A1: a in Q;
  Q in X;
  hence thesis by A1, TARSKI:def 4;
end;
