And this is where all the confusion starts, as in all aviation "it depends" on how ahead or behind your certifying authority are in the PBN world.
RNAV (RNP) is not equal to RNP APCH, it is similar in many respects but it is certainly not SAAAR or RNAV (RNP AR) or RNP AR APCH (three names for the same approach by different states).
RNAV (RNP) is not part of the ICAO PBN structure. It was an attempt to allow such equipped aircraft to operate using the current aircraft navigation capability. As such in some states RNAV (RNP) was able to be flown without GNSS, but required Radar monitoring, however many states decided (quite rightly in my view) that GNSS should be part of the aircraft system requirements. RNAV (RNP) did not have RF legs or an RNP less that 0.3:
RNAV (RNP AR), SAAAR or RNP AR APCH can have RF legs, could be below 0.3 and could be either public or tailored (private) for specific requirements.
The whole PBN debacle of nomenclature, sensor requirements etc was the result of the US and Europe heading for similar outcomes via different pathways and the slow cumbersome nature of ICAO to develop a standard.
As the ICAO contracting states start towards PBN standardisation most of the confusion "should" disappear.
The USA name for RNP AR APCH was SAAAR (three A's) Aircraft, Aircrew Authorisation.
If it says RNAV (RNP) you certainly cannot continue without dual GPS
My regulator: you cannot
start an RNP AR APCH approach without Dual GNSS but after the FF you can continue with a single GNSS.