\b1 b2 e -> unionbag (unionbag b1 (singletonbag e)) b2 ===[use assoc/comm (step 1) \b1 b2 e -> unionbag (unionbag (singletonbag e) b1) b2 ===[apply catalog bag.thy (step 2) \b1 b2 e -> nonemptybag e (unionbag b1 b2)