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 Th67:
  for T, A, F holds T-tail F in (Polish-WFF-set(T, A))^^Polish-arity F
proof
  let T, A, F;
  consider n, t, u such that
      A1: t in T and
      A2: n = A.t and
      A3: u in Polish-WFF-set(T, A)^^n and
      A4: F = t^u by Th32;
  T-head F = t & T-tail F = u by A1, A4, Th52;
  hence thesis by A2, A3;
end;
