
theorem bag1a:
for Z being non empty set, B1,B2 being bag of Z
holds B1 divides B2 iff ex B3 being bag of Z st B2 = B1 + B3
proof
let Z be non empty set, b1,b2 be bag of Z;
now assume A: b1 divides b2;
  b1 + (b2 -' b1) = b2 by A,PRE_POLY:47;
  hence ex b3 being bag of Z st b2 = b1 + b3;
  end;
hence thesis by PRE_POLY:50;
end;
