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 Th73:
  (for n holds scf(r).n>0) implies cocf(r).2 = scf(r).0 + 1 / (scf
  (r).1 + 1/scf(r).2)
proof
  set s=scf(r);
A1: cocf(r).2 =c_n(r).2 * ((c_d(r))").2 by SEQ_1:8
    .=c_n(r).2 * (c_d(r).2)" by VALUED_1:10
    .=c_n(r).2 *(1/c_d(r).2)
    .=c_n(r).2 /c_d(r).2;
  assume
A2: for n holds scf(r).n>0;
  then
A3: s.1>0;
A4: c_d(r).2 =s.(0+2)*c_d(r).(0+1) + c_d(r).0 by Def6
    .=s.2*s.1+c_d(r).0 by Def6
    .=s.2*s.1+1 by Def6;
A5: c_n(r).2 =s.(0+2) * c_n(r).(0+1) + c_n(r).0 by Def5
    .=s.2*(s.1 * s.0 +1) +c_n(r).0 by Def5
    .=s.2 * s.1 * s.0 +s.2 +s.0 by Def5;
A6: s.2>0 by A2;
  then s.0 + 1/(s.1+1/s.2) =s.0+1/((s.1 * s.2 +1)/ s.2) by XCMPLX_1:113
    .=s.0 + s.2/(s.1 * s.2 +1) by XCMPLX_1:57
    .=(s.0 * (s.1 * s.2 +1) + s.2)/(s.1 * s.2 +1) by A3,A6,XCMPLX_1:113
    .=cocf(r).2 by A1,A5,A4;
  hence thesis;
end;
