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 Th72:
  scf(r).1 <> 0 implies cocf(r).1 = scf(r).0 + 1 / scf(r).1
proof
  set s=scf(r);
  assume
A1: scf(r).1<>0;
  thus cocf(r).1 = c_n(r).1 * ((c_d(r))").1 by SEQ_1:8
    .=c_n(r).1 * (c_d(r).1)" by VALUED_1:10
    .=c_n(r).1 *(1/c_d(r).1)
    .=c_n(r).1 /c_d(r).1
    .=(s.1 * s.0 +1) / c_d(r).1 by Def5
    .=(s.1 * s.0 +1) / s.1 by Def6
    .=s.0 +1 / s.1 by A1,XCMPLX_1:113;
end;
