DW 2nd High Loop?

[Triumph TT]

I've searched here and the web and I cannot find a definite answer...

I am installing a dw in an island. The P-trap is under the floor with a fitting poking through the floor to attach the dw hose to. The dw has a "high loop" factory installed on the side. The kitchen sink, opposite the dw, has a air admittance valve installed and the dw ties into the line after the sink under the floor. Do I still need an additional high loop under the island if the machine has one already?

Thank you.

 

[Smooky]

If it is going to be inspected the inspector may want to see the high loop. I would drill the hole at the top of the cabinet and run the pipe through and then it would be no question.
Your code might be different but here is what ours says:
The waste line of a domestic dishwashing machine discharging into a kitchen sink tailpiece or food waste grinder shall connect to a deck-mounted air gap or the waste line shall rise and be securely fastened to the underside of the sink rim or counter.