theorem
  k <= n implies m |^ k divides m |^ n
proof
  assume k <= n;
  then consider t being Nat such that
A1: n = k + t by NAT_1:10;
  reconsider t as Element of NAT by ORDINAL1:def 12;
  m |^ n = (m |^ k)*(m |^ t) by A1,Th8;
  hence thesis by NAT_D:def 3;
end;
