Crossword Genius

Equine service provider extremely involved in lean fit (6,6)

Ross

I believe the answer is:

livery stable

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'equine service provider' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'extremely involved in lean fit' is the wordplay.
'extremely' becomes 'very' (very can mean extremely or considerably).
'involved in' indicates putting letters inside.
'lean' becomes 'list' (both can mean to tilt).
'fit' becomes 'able' (similar in meaning).
'very' going into 'list' is 'liveryst'.
'liveryst'+'able'='LIVERY-STABLE'

Can you help me to learn more?

(Other definitions for livery stable that I've seen before include "Equine establishment" , "place where horses may be kept" , "Equine business" .)

I've seen this clue in The Telegraph.
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