theorem Th37:
  for P, A, Q st Q is A-closed holds Polish-expression-set(P, A) c= Q
proof
  let P, A, Q;
  assume A1: Q is A-closed;
  let a;
  assume a in Polish-expression-set(P, A);
  then consider n such that A2: a in Polish-expression-hierarchy(P, A, n+1)
      by Th28;
  thus thesis by A1, A2, Th35, TARSKI:def 3;
end;
