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

theorem Th29:
  Sum sqr cosec x_r-seq(m) = 2*m*(2*m+2)/6
  proof
    set f = x_r-seq(m);
A1: len sqr cot f = len cot f by CARD_1:def 7
    .= len f by CARD_1:def 7
    .= m by BASEL_1:21;
A2: Sum(1+sqr cot f) = (1*len sqr cot f) + Sum(sqr cot f) by BASEL_1:4;
    Sum(sqr cot f) = 2*m*(2*m-1)/6 by Th28;
    hence thesis by A1,A2,BASEL_1:26;
  end;
