theorem Th16:
  r is irrational & n is even & n > 0 implies
    r > c_n(r).n/c_d(r).n
  proof
    assume
A1: r is irrational;
    assume
A2: n is even;
    assume n > 0; then
    reconsider m = n -1 as odd natural number by A2;
    (c_d(r).(m+1)*(c_d(r).(m+1)*rfs(r).(m+2) + c_d(r).m)) > 0 by A1,Th13;
    then (-1)|^m
     /(c_d(r).(m+1)*(c_d(r).(m+1)*rfs(r).(m+2) + c_d(r).m)) < 0; then
    c_n(r).(m+1)/c_d(r).(m+1) - r < 0 by A1,Th15; then
    c_n(r).(n-1+1)/c_d(r).(n-1+1) -r + r < 0 + r by XREAL_1:8;
    hence thesis;
  end;
