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 Th66:
  c_n(r).(n+2)*c_d(r).n - c_n(r).n*c_d(r).(n+2) = (-1)|^n * scf(r) .(n+2)
proof
  set s1=c_n(r), s2=c_d(r), s=scf(r);
  s1.(n+2)*s2.n-s1.n*s2.(n+2) =(s.(n+2)*s1.(n+1)+s1.n)*s2.n-s1.n*s2.(n+2)
  by Def5
    .=(s.(n+2)*s1.(n+1)+s1.n)*s2.n-s1.n*(s.(n+2)*s2.(n+1)+s2.n) by Def6
    .=s.(n+2)*(s1.(n+1)*s2.n-s1.n*s2.(n+1))
    .=(-1)|^n * s.(n+2) by Th64;
  hence thesis;
end;
