reserve m, n for Nat;

theorem Th15:
  for n being non zero Nat, p being Prime
   st not p in support ppf n holds p |-count n = 0
proof
  let n be non zero Nat, p be Prime;
  assume
A1: not p in support ppf n;
  assume p |-count n <> 0;
  then (ppf n).p = p |^ (p |-count n) by NAT_3:56;
  hence thesis by A1,PRE_POLY:def 7;
end;
