reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem Th35:
  a > n & n <> 0 implies (pfexp n).a = 0
proof
  assume
A1: a > n & n <> 0;
  reconsider a as Element of NAT by ORDINAL1:def 12;
  per cases;
  suppose
    a is not prime;
    then not a in dom pfexp n by Th33;
    hence thesis by FUNCT_1:def 2;
  end;
  suppose
A2: a is prime;
    then a <> 1;
    then a |-count n = 0 by A1,Th23;
    hence thesis by A2,Def8;
  end;
end;
