theorem
  for p be prime Nat, a be non trivial Nat holds
    (p |-count a)*(a |-count p|^n) <= n
proof
  let p be prime Nat, a be non trivial Nat;
  A1: p > 1 by NAT_4:14;
  p|^((p |-count a)*(a |-count p|^n)) <= p|^n by Count7;
  hence thesis by A1,PEPIN:66;
end;
