
theorem Th16:
  for p being Prime, a being Element of NAT st a <> 0 holds
  1 <= p |^ (p |-count a) <= a
proof
  let p be Prime, a be Element of NAT;
  assume
A1: a<>0;
  set x = p |^ (p |-count a);
  p >= 1 by INT_2:def 4;
  hence 1 <= x by PREPOWER:11;
  p <> 1 by INT_2:def 4;
  then x divides a by A1,NAT_3:def 7;
  hence thesis by A1,NAT_D:7;
end;
