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
  c_n(r).(n+2) / c_d(r).(n+2) = (scf(r).(n+2) * c_n(r).(n+1) + c_n(r).n)
  / (scf(r).(n+2) * c_d(r).(n+1) + c_d(r).n)
proof
  c_n(r).(n+2) = scf(r).(n+2) * c_n(r).(n+1) + c_n(r).n by Def5;
  hence thesis by Def6;
end;
