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;
