Martinez v. Ryan

My SCOTUSblog case was Martinez v. Ryan case. Some background information on this case is that Martinez is serving 2 consecutive sentences for having sex with a person under the age of 15. Martinez filed for a direct appeal with the help of a state appointed counsel. But the Arizona Supreme Court denied him.
The question is if the the prisoners have the right to argue that their lawyers were inadequate during post-conviction proceedings, does the the defendant have a right to appointed counsel during that proceeding? Or in other words he has a right to an effective assistance of post-conviction counsel in raising his ineffective-assistance-of-trial-counsel claim. Martinez knows he has this right so he is trying to get an appeal so that things may be reconsidered. Arizona is arguing the whole right to counsel or lack there of as an opinion and that recognition should have been made prior to of the fact that the counsel was ineffective. In my opinion I don't think they will rule in his favor because it seems as though their mind is already made up. But I think that they will at least consider the constitution but still decide against it and go with the state's rules. This case is still pending.