Induplicate/reduplicate refers to the how a leaflet is attached to the rachis ... Induplicate leaflets attached with a V and reduplicate leaves attach with upside-down-V (or A for want of a better keyboard symbol).
In fact image 5524 shows these leaflets attach with an inverted V = reduplicate ... sorry I missed it before.
Anyways ... this arrangement seen in the Cocosoideae sub-family or the Arecoidae sub-family ... hence helpful in eliminating the three other sub-families (which have induplicate leaves).
SO we know its got to be from either of these two sub-families ... choices are narrowing .........................................................
mmmm .... bingo ..... Rhopalostylis sapida (Nikau Palm) ... a NZ native Palm
Rhopalostylis sapida - Google Search PlantFiles: Pictures of Shaving Brush Palm, Nikau Palm (Rhopalostylis sapida)