What is the ruling regarding the liability and manumission of two slaves sharing injury liability when one injures the other while both belong to the same master?

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When a master frees two slaves simultaneously, valued at 100 and 150 units respectively, and the cheaper slave injures the more valuable one, reducing the latter's value by one-third and incurring corresponding *arsh* (compensation) during the master's lifetime, and then both slaves die, a lottery (*qur'a*) is cast between them to determine the extent of manumission and liability. If the lottery falls upon the injurer, four-fifths of him is manumitted, and he owes four-fifths of the *arsh* for his injury. The heirs of the master retain one-fifth of the injurer and the full value of the injured slave, totaling 160 units, which equals the amount freed from the injurer. This distribution is derived from a calculation where the injury equals half the value of the injured slave, leaving half for the master. The remaining value of both slaves equals two full shares, meaning the freed portion is four-fifths of one share. If the lottery falls upon the injured slave, one-third of him is manumitted. He is owed one-third of the *arsh*, which becomes a lien on the neck of the injurer, amounting to one-ninth of the full blood-price (*diyah*). This arises because injury inflicted upon one whose person is partly free and partly enslaved generates liability proportionate to the degree of enslavement. The owed *arsh* exhausts the value of the injurer slave, so the master only retains manumission for one-third of the injured slave, with the other two-thirds remaining enslaved.