reserve k,m,n for Nat;
reserve R for commutative Ring,
        p,q for Polynomial of R,
        z0,z1 for Element of R;

theorem Th32:
  Sum Basel-seq = PI^2/6
  proof
    for n holds Basel-seq1.n <= Partial_Sums Basel-seq.n &
    Partial_Sums Basel-seq.n <= Basel-seq2.n
    proof
      let n;
      Sum(Basel-seq,n) = Sum(Basel-seq,n);
      hence thesis by Th30,Th31;
    end;
    hence thesis by SEQ_2:20,BASEL_1:34;
  end;
