theorem Th23:
  for P, A, n holds Polish-expression-hierarchy(P, A, n+1)
      = Polish-expression-layer(P, A, Polish-expression-hierarchy(P, A, n))
proof
  let P, A, n;
  consider U such that
  A1: U = Polish-expression-hierarchy(P, A, n) and
  A2: Polish-expression-hierarchy(P, A, n+1)
          = Polish-expression-layer(P, A, U) by Def9;
  thus thesis by A1, A2;
end;
