Crossword Genius

French duke indeed worked out! (7)


I believe the answer is:


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'worked out' is the definition.
(I've seen this before)

'french duke indeed' is the wordplay.
I cannot really see how this works, but
'duke' could be 'd' (abbreviation) and 'd' is located in the answer.
The remaining letters 'educed' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for deduced that I've seen before include "Gathered" , "Inferred" , "Worked out by reasoning" , "Came to logical conclusion like Sherlock" , "Arrived at by reasoning" .)

I've seen this clue in The Sun.
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