Crossword Genius

At the end, demote member in rank? (8)

Ross

I believe the answer is:

relegate

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'at the' is the definition.
I can't tell whether this defines the answer.

'end demote member in rank?' is the wordplay.
'end' says to take the final letters.
'member' becomes 'leg' (member can mean a limb).
'in' means one lot of letters goes inside another.
'rank?' becomes 'rate' ('rate' can be a synonym of 'rank').
The final letter of 'demote' is 'e'.
'e'+'leg'='eleg'
'eleg' going into 'rate' is 'RELEGATE'.

Can you help me to learn more?

(Other definitions for relegate that I've seen before include "Demote" , "Transfer to a lower division" , "Move to a lower division" , "Move down to a lower grade" , "Send down" .)

I've seen this clue in The Independent.
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