
theorem Th3:
  for X being set, b1,b2 being bag of X holds b1 divides lcm(b1,b2)
  & b2 divides lcm(b1,b2)
proof
  let X be set, b1,b2 be bag of X;
  set bb = lcm(b1,b2);
  now
    let k be object;
    b1.k <= max(b1.k,b2.k) by XXREAL_0:25;
    hence b1.k <= bb.k by Def2;
  end;
  hence b1 divides lcm(b1,b2) by PRE_POLY:def 11;
  now
    let k be object;
    b2.k <= max(b1.k,b2.k) by XXREAL_0:25;
    hence b2.k <= bb.k by Def2;
  end;
  hence thesis by PRE_POLY:def 11;
end;
