theorem Th44:
  m divides n iff m lcm n = n
proof
  thus m divides n implies m lcm n = n
  proof
    set M = m lcm n;
    assume m divides n;
    then
A1: M divides n by NAT_D:def 4;
    n divides M by NAT_D:def 4;
    hence thesis by A1,NAT_D:5;
  end;
  thus thesis by NAT_D:def 4;
end;
