
theorem
  for a be heavy positive Real holds (1/(a+1)) + (1/(a-1)) > 2/a
  proof
    let a be heavy positive Real;
    A1: (1*(a+1))/((a-1)*(a+1)) = 1/(a-1) &
    (1*(a-1))/((a-1)*(a+1)) = 1/(a+1) & (2*a)/(a*a) = 2/a by XCMPLX_1:91;
    1 - 1 < a*a - 1 < a*a - 0 by XREAL_1:6; then
    ((a+1)+(a-1))/((a+1)*(a-1)) > ((a+1)+(a-1))/(a*a) by XREAL_1:76;
    hence thesis by A1;
  end;
