theorem Th21:
  for P, A, U, u st u in Polish-expression-layer(P, A, U)
      ex p, q st p in P & u = p^q
  proof
  let P, A, U, u;
  assume u in Polish-expression-layer(P, A, U);
  then consider p, q, n such that
  A1: u = p^q & p in P and
      n = A.p & q in U^^n by Def6;
  thus thesis by A1;
  end;
