Crossword Genius

A life of someone by himself? (13)

Ross

I believe the answer is:

autobiography

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

'a life of someone by' is the wordplay.
'a life' becomes 'biography' ('biography' can be a synonym of 'life').
'of someone' becomes 'auto' (I am not sure about this - if you are sure you should believe this answer much more).
'by' is a charade indicator (letters next to each other).
'biography' after 'auto' is 'AUTOBIOGRAPHY'.

Can you help me to learn more?

(Other definitions for autobiography that I've seen before include "Memoirs" , "A person's account of their life" , "Story of one's life" , "Person's life story written by the subject" , "Personal account of one's life" .)

I've seen this clue in The Times.
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