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*;
reserve k,l,m,n,i,j for Nat,
  a, b, c for object,
  x, y, z, X, Y, Z for set,
  D, D1, D2 for non empty set;
reserve p, q, r, s, t, u, v for FinSequence;
reserve P, Q, R for FinSequence-membered set;
reserve B, C for antichain;
reserve S, T for Polish-language;
reserve A for Polish-arity-function of T;
reserve U, V, W for Polish-language of T;
reserve F, G for Polish-WFF of T, A;

theorem Th71:
  for T, A, F, n st F in Polish-expression-hierarchy(T, A, n+1) holds
      rng Polish-WFF-args F c= Polish-expression-hierarchy(T, A, n)
proof
  let T, A, F, n;
  assume F in Polish-expression-hierarchy(T, A, n+1);
  then reconsider G = F as Element of Polish-expression-hierarchy(T, A, n+1);
  rng Polish-WFF-args F = rng Polish-WFF-args G by Th60, Th26;
  hence thesis by FINSEQ_1:def 4;
end;
