 reserve n,i for Nat;
 reserve p for Prime;

theorem Ciek: :: MOEBIUS1:9 inverted
  n <> 0 & (p |^ i) divides n implies i <= p |-count n
  proof
    assume A0: n <> 0;
    assume A1: (p |^ i) divides n;
    reconsider b = p |^ i as non zero Nat;
    reconsider a = n as non zero Nat by A0;
    p |-count b <= p |-count a by A1,NAT_3:30;
    hence thesis by NAT_3:25,INT_2:def 4;
  end;
