Is become a stream-enterer (sotāpanna) enough?
The Pali word translated as "existence" is "bhava". "Bhava" is a mental asava (defilement) and not another life. There are 10 fetters to break through for Arahantship. The stream-enterer has broken three fetters. Each fetter is a type of becoming. Therefore, the sutta says "they do not take up an eighth becoming" because there are only a maximum of 7 more fetters to break..  

In summary, it is pointless asking about stream-entry if you believe in reincarnation because this just perpetuates the "self-view" that must be broken for stream-entry. When there is the belief in reincarnation, it is the belief of "I will reincarnated or reborn seven more times". This is self-view. 

The stream-enterer, in the suttas, has the realisation of: "All that is subject to arising is subject to cessation". The realisation of the stream-enterer is not: "All that is subject to cessation is subject to re-arising".