reserve m, n for Nat;

theorem Th9:
  for p being Prime st n <> 0 & m <= p |-count n holds p |^ m divides n
proof
  let p be Prime;
  assume that
A1: n <> 0 and
A2: m <= p |-count n;
A3: p |^ m divides p |^ (p |-count n) by A2,NEWTON:89;
  p > 1 by INT_2:def 4;
  then p |^ (p |-count n) divides n by A1,NAT_3:def 7;
  hence thesis by A3,NAT_D:4;
end;
