theorem Th68:
  for T, A, n for F being Element of Polish-expression-hierarchy(T, A, n+1)
    holds T-tail F in Polish-expression-hierarchy(T, A, n)^^Polish-arity F
proof
  let T, A, n;
  let F be Element of Polish-expression-hierarchy(T, A, n+1);
  set U = Polish-expression-hierarchy(T, A, n);
  F in Polish-expression-hierarchy(T, A, n+1);
  then F in Polish-expression-layer(T, A, U) by Th23;
  then consider t being Element of T, u being Element of T* such that
  A2: F = t^u and
  A3: u in U^^(A.t) by Def19;
  thus thesis by A2, A3;
end;
