
theorem Th7:
  for X being set, b1,b2 be bag of X holds b2 divides b1 iff lcm( b1,b2) = b1
proof
  let X being set, b1,b2 be bag of X;
  now
    assume
A1: b2 divides b1;
    for k being object holds b1.k = max(b1.k,b2.k)
           by XXREAL_0:def 10,A1,PRE_POLY:def 11;
    hence lcm(b1,b2) = b1 by Def2;
  end;
  hence thesis by Th3;
end;
