Is a slave woman's child ruled to belong to the claimant if the testimony states she was the claimant's slave's daughter?

Primary text

If a man claims ownership of a female slave, and witnesses testify that she is the daughter of his slave woman, ownership is not granted to the claimant based on this testimony alone. This is because the birth may have occurred before he acquired the mother. If the testimony specifies that the birth occurred while the slave was within his possession, ownership is established, because the offspring is considered a product (*nama'*) of his property, and the product belongs to the owner unless a cause that transfers it exists. This is distinguished from prior proof of ownership because the product is secondary to the original property; establishing ownership of the product in the past follows from establishing ownership of the original item at that time. Furthermore, the testimony here established the cause of ownership (the birth within his possession), which strengthens the claim, similar to testimony establishing a past transaction like lending or selling.