Crossword Genius

Green stuff eaten (not “ate”) up in desert (5)

Ross

I believe the answer is:

negev

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'desert' is the definition.
(I know that Negev is a desert)

'green stuff eaten not ate up' is the wordplay.
'green stuff' becomes 'veg' (I can't justify this - if you can you should believe this answer much more).
'not' suggests deleting specific letters.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'eaten' with 'ate' taken away is 'en'.
'veg'+'en'='vegen'
'vegen' reversed gives 'NEGEV'.

'in' is the link.

Can you help me to learn more?

(Other definitions for negev that I've seen before include "part of Israel" , "Wilderness" , "Israeli desert area abutting Sinai" , "Southern Israeli desert" , "Desert region in Israel" .)

I've seen this clue in The Times.
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