This bathroom was already plumbed before I bought the house.  I am adding a sink (wet bar) to the right of the bathroom.  I am wanting to drain the sink into the pipe that has a green inspection sticker on it.  I "think" that pipe is a vent pipe tying into the vent that goes up on the right side of the picture.  Does this pipe with the green sticker vent the toilet?  I mocked up a few pipes to show what I want to do.  I basically want the drain to come out of that green labeled pipe to the right, bend behind the tub and come out at the base of the tube.  There it will split to vent up to the top of the joists where it cuts over one joist then runs back to the top of the vent pipe.  The drain will simply come out the side for a future bar sink.

Is this an okay way to drain a sink?  

Here's the bathroom


Here's showing the drain line I want to run mocked up and how I will connect it. (There is a slope down to the drain the entire run but it's hard to see in pics)



This pic shows the back side of the tub.  There is a slight void that will allow me to run the pipes easily.



Last shows the vent going into the joists.  It cuts over one then I need to get another elbow and run it back to that back pipe on the wall.

Not if you were in WI. (or AZ, CO, and MN)