reserve m, n for Nat;

theorem Th48:
  for p being Prime, n being non zero Nat holds p
  |-count n = 0 implies (PFactors n).p = 0
proof
  let p be Prime, n be non zero Nat;
  assume p |-count n = 0;
  then (pfexp n).p = 0 by NAT_3:def 8;
  then not p in support pfexp n by PRE_POLY:def 7;
  then not p in support PFactors n by Def6;
  hence thesis by PRE_POLY:def 7;
end;
