Tell me what I am not seeing here? This is plumbing under the kitchen sink at island. Thanks
This may help
That’s a good way to vent that trap…SIGH!!! It would be nice to see one like that. Did a $350,000 home with an island sink yesterday…didn’t look like that under the sink!!
Here’s an even better one…diagram only:
http://www.longbeach.gov/civica/filebank/blobdload.asp?BlobID=17060
The cleanout at the vertical wall vent pipe allows for cleaning the horizontal vent run if it ever gets blocked due to a sewer backup, etc.
If your jurisdiction follows the UPC, then you have an improper installation there. Two traps are not allowed to share one trap arm under the UPC.
Jephrey is correct. The arrangement is wrong and will need corrected.
Adding to this is it will most likely cause trouble because it is feeding from a garburator increasing the speed of discharge. This will create suction on the one trap which will no longer function as a trap.
Thats a really good image you posted Micheal, do you mind me asking where you obtained it? Plumbing is my weak spot and I would like to see more images such as these. They are so much more informative than drawings.
On the back side of that double wye, what’s connected? Is it just capped?
I rarely see the set-up like in Mikes photo. These days all I see is AAV’s.
Not if your on IRC based codes like most of the country. Also I see both on the same trap arm all the time, and this question/topic has come up before.
According to plumbers I have asked, having a garbulator and sink on the same trap arm is no more problematic than having each one with it’s own trap arm connected to the same line, as long as it is done correctly. And the garbulator drain connections are sized to not completely fill the trap arm and branch pipe … 
The only issue I have is that any garbage disposal unit can have a negitive impact on any on-site septic disposal system.
JMO & 2-Nickels …
Both on the same trap is correct.
We are dealing with the designed one in the picture that is wrong.
Yes, I meant trap arm … fixed … :D.
The IRC permits both to be connected to one trap arm … http://publicecodes.citation.com/icod/irc/2009/icod_irc_2009_31_sec007.htm