reserve a, b, k, n, m for Nat,
  i for Integer,
  r for Real,
  p for Rational,
  c for Complex,
  x for object,
  f for Function;
reserve l, n1, n2 for Nat;
reserve s1, s2 for Real_Sequence;

theorem
  (for n holds c_d(r).n<>0) implies c_n(r).(n+2)/c_d(r).(n+2) - c_n(r).n
  /c_d(r).n = (-1)|^n * scf(r).(n+2) / (c_d(r).(n+2) * c_d(r).n)
proof
  set s1=c_n(r), s2=c_d(r), s=scf(r);
  assume for n holds s2.n<>0;
  then s2.n<>0 & s2.(n+2)<>0;
  then
  s1.(n+2)/s2.(n+2) - s1.n/s2.n =(s1.(n+2) * s2.n - s1.n * s2.(n+2))/(s2.(
  n+2) * s2.n) by XCMPLX_1:130
    .=(-1)|^n * s.(n+2)/(s2.(n+2) * s2.n) by Th66;
  hence thesis;
end;
