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
  for T, A, F st T-head F in Polish-atoms(T, A) holds F = T-head F
proof
  let T, A, F;
  assume T-head F in Polish-atoms(T, A);
  then Polish-arity F = 0 by Def7;
  then T-tail F in Polish-WFF-set(T, A)^^0 by Th67;
  then T-tail F in {{}} by Th6;
  then T-tail F = {} by TARSKI:def 1;
  then F = (T-head F)^{};
  hence thesis by FINSEQ_1:34;
end;
