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

theorem Th55:
  p |-count n = 0 implies (ppf n).p = 0
proof
  assume p |-count n = 0;
  then (pfexp n).p = 0 by Def8;
  then not p in support pfexp n by PRE_POLY:def 7;
  then not p in support ppf n by Def9;
  hence thesis by PRE_POLY:def 7;
end;
