Oversight AI + Emergency Shutdown

By JamesBond, in Android: Netrunner Rules Questions

So if a piece of ICE has Oversight AI on it, and the runner uses Emergency Shutdown to derez that pice of ICE, what happens?

I'm assuming the the ICE derezzes normally and that Oversight AI stays on the ICE (because it is a condition counter now). So that if the Corp player rezzes the ICE again, then the Oversight AI condition would still be in effect, meaning that if the Runner later broke all the subroutines in a single run, then the ICE would be trashed.

Is this correct?

JamesBond said:

So if a piece of ICE has Oversight AI on it, and the runner uses Emergency Shutdown to derez that pice of ICE, what happens?

I'm assuming the the ICE derezzes normally and that Oversight AI stays on the ICE (because it is a condition counter now). So that if the Corp player rezzes the ICE again, then the Oversight AI condition would still be in effect, meaning that if the Runner later broke all the subroutines in a single run, then the ICE would be trashed.

Is this correct?

Sounds right to me.