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;

theorem Th29:
  rfs(i).(n+1) = 0
proof
  defpred P[Nat] means rfs(i).($1+1) = 0;
A1: rfs(i).0 = i by Def3;
A2: for n st P[n] holds P[n+1]
  proof
    let n such that
A3: P[n];
    thus rfs(i).(n+1+1) = 1 / frac(rfs(i).(n+1)) by Def3
      .= 1/(0-0) by A3
      .= 0;
  end;
  rfs(i).(0+1) = 1 / frac(rfs(i).0) by Def3
    .= 1/(i-i) by A1
    .= 0;
  then
A4: P[0];
  for n holds P[n] from NAT_1:sch 2(A4,A2);
  hence thesis;
end;
