theorem
  n divides m & k divides m iff n lcm k divides m
proof
  n lcm k divides m implies n divides m & k divides m
  proof
    set M = n lcm k;
A1: n divides M by NAT_D:def 4;
A2: k divides M by NAT_D:def 4;
    assume n lcm k divides m;
    hence thesis by A1,A2,NAT_D:4;
  end;
  hence thesis by NAT_D:def 4;
end;
